James Franck was born in Hamburg, Germany, on 26 August 1882, the second child and first son of Jacob Franck, a banker, and his wife Rebecca née Nachum Drucker. He had an older sister, Paula, and a younger brother, Robert Bernard. His father was a devout and religious man, while his mother came from a family of rabbis. Franck attended primary school in Hamburg. Starting in 1891 he attended the Wilhelm-Gymnasium, which was then a boys-only school.

Hamburg had no university then, so prospective students had to attend one of the 22 universities elsewhere in Germany. Intending to study law and economics, Franck entered the University of Heidelberg in 1901, as it had a renowned law school. He attended lectures on law, but was far more interested in those on science. While there, he met Max Born, who would become a lifelong friend. With Born's help, he was able to persuade his parents to allow him to switch to studying physics and chemistry. Franck attended mathematics lectures by Leo Königsberger and Georg Cantor, but Heidelberg was not strong on the physical sciences, so he decided to go to the Frederick william University in Berlin.

At Berlin, Franck attended lectures by Max Planck and Emil Warburg. On 28 July 1904 he saved a pair of children from drowning in the Spree River. For his Doctor of Philosophy (Dir. Phil.) under Warburg's supervision, Warburg suggested that he study corona discharges. Franck found this topic too complex, so he changed the focus of his thesis. Entitled Über der Beweglichkeit Ladungsträger der Spitzenentladung ("On the Mobility of Ions"), it would subsequently be published in the Annalen der Physik.

With his thesis completed, Franck had to perform his deferred military Service. He was called up on 1 October 1906 and joined the 1st Telegraph Battalion. He suffered a minor horse riding accident in December and was discharged as unfit for duty. He took up an assistantship at the Physikalische Verein in Frankfurt in 1907, but did not enjoy it, and soon returned to Frederick william University. At a concert Franck met Ingrid Josephson, a Swedish Pianist. They were married in a Swedish ceremony in Gothenburg on 23 December 1907. They had two daughters, Dagmar (Daggie), who was born in 1909, and Elisabeth (Lisa), who was born in 1912.

To pursue an academic career in Germany, having a doctorate was not enough; one needed a venia legendi, or habilitation. This could be achieved with either another major thesis or by producing a substantial body of published work. Franck chose the latter route. There were many unsolved problems in physics at the time, and by 1914 he had published 34 articles. He was the sole author of some, but generally preferred working in collaboration with Eva von Bahr, Lise Meitner, Robert Pohl, Peter Pringsheim (de), Robert W. Wood, Arthur Wehnelt or Wilhelm Westphal. His most fruitful collaboration was with Gustav Hertz, with whom he wrote 19 articles. He received his habilitation on 20 May 1911.

In 1914, Franck teamed up with Hertz to perform an experiment to investigate fluorescence. They designed a vacuum tube for studying energetic electrons that flew through a thin vapour of mercury atoms. They discovered that when an electron collided with a mercury atom it could lose only a specific quantity (4.9 electron volts) of its kinetic Energy before flying away. A faster electron does not decelerate completely after a collision, but loses precisely the same amount of its kinetic Energy. Slower electrons just bounce off mercury atoms without losing any significant speed or kinetic Energy.

Franck enlisted in the German Army soon after the outbreak of the First World War in August 1914. In December he was sent to the Picardy sector of the Western Front. He became a deputy officer (offizierstellvertreter), and then a lieutenant (leutnant) in 1915. In early 1915 he was transferred to Fritz Haber's new unit that would introduce clouds of chlorine gas as a weapon. With Otto Hahn he was responsible for locating sites for the attacks. He was awarded the Iron Cross, Second Class, on 30 March 1915, and the city of Hamburg awarded him the Hanseatic Cross on 11 January 1916. While in hospital with pleurisy, he co-wrote yet another scientific paper with Hertz, and he was appointed an assistant professor in his absence by Frederick william University on 19 September 1916. Sent to the Russian front, he came down with dysentery. He returned to Berlin, where he joined Hertz, Westphal, Hans Geiger, Otto Hahn and others at Haber's Kaiser Wilhelm Institute for Physical Chemistry and Electrochemistry, working on the development of gas masks. He was awarded the Iron Cross, First Class, on 23 February 1918. He was discharged from the Army on 25 November 1918, soon after the war ended.

Under Born and Franck, Göttingen was one of the world's great centres for physics between 1920 and 1933. Although they published only three papers together, Born and Franck discussed every one of their papers with each other. Gaining admittance to Franck's laboratory became highly competitive. His doctoral students included Hans Kopfermann, Arthur R. von Hippel, Wilhelm Hanle, Fritz Houtermans, Heinrich Kuhn, Werner Kroebel (de), Walter Lochte-Holtgreven and Heinz Maier-Leibnitz. In supervising doctoral candidates, Franck had to ensure that thesis topics were well-defined, and would teach the candidate how to conduct original research, while still staying within the limits of the candidate's ability, the laboratory's equipment and the institute's budget. Under his direction, research was carried out into the structure of atoms and molecules.

In a second paper presented in May 1914, Franck and Hertz reported on the light emission by the mercury atoms that had absorbed Energy from collisions. They showed that the wavelength of this ultraviolet light corresponded exactly to the 4.9 eV of Energy that the flying electron had lost. The relationship of Energy and wavelength had also been predicted by Bohr. Franck and Hertz completed their last paper together in December 1918. In it, they reconciled the discrepancies between their results and Bohr's theory, which they now acknowledged. In his Nobel lecture, Franck admitted that it was "completely incomprehensible that we had failed to recognise the fundamental significance of Bohr’s theory, so much so, that we never even mentioned it once". On 10 December 1926, Franck and Hertz were awarded the 1925 Nobel Prize in Physics "for their discovery of the laws governing the impact of an electron upon an atom.".

Franck assisted Frederick Lindemann in helping dismissed Jewish Scientists find work overseas, before he left Germany in November 1933. After a brief visit to the United States, where he measured the absorption of light in heavy water with Wood at Johns Hopkins University, he took up a position at the Niels Bohr Institute in Copenhagen. He needed a new collaborator, so he took on Hilde Levi, whose recent thesis had impressed him. His original intention was to continue his research into the fluorescence of vapours and liquids, but under Bohr's influence they began to take an interest in biological aspects of these reactions, particularly photosynthesis, the process by which plants use light to convert carbon dioxide and water into more organic compounds. Biological processes turned out to be far more complicated than simple reactions in atoms and molecules. He co-authored two papers with Levi on the subject, which he would return to over the following years.

In 1935, Franck moved to the United States, where he had accepted a professorship at Johns Hopkins University. The laboratory there was poorly equipped compared to the one in Göttingen, but he received $10,000 for equipment from the Rockefeller Foundation. A more intractable Problem was that the university had no money to hire skilled staff. Franck was concerned about his family members remaining in Germany, and needed money to help them emigrate. He therefore accepted an offer from the University of Chicago, where his work on photosynthesis had attracted interest, in 1938.

Franck found a position at the Polytekniske Læreanstalt in Copenhagen for Arthur von Hippel, who was now his son in law, having married his daughter Dagmar. He decided to provide financial security for his children by dividing his Nobel Prize money between them. The gold medal itself was entrusted to Niels Bohr for safekeeping. When Germany invaded Denmark on 9 April 1940, the Hungarian Chemist George de Hevesy dissolved the gold medal, along with that of Max von Laue in aqua regia to prevent the Germans from taking them. He placed the resulting solution on a shelf in his laboratory at the Niels Bohr Institute. After the war, he returned to find the solution undisturbed and precipitated the gold out of the acid. The Nobel Society then recast the Nobel Prize medals.

Franck's first paper there, co-authored with Edward Teller, was on photochemical processes in crystals. Hans Gaffron became his collaborator. They were joined by Pringsheim, who escaped from Belgium after the German invasion. Franck arranged a position for Pringsheim at his laboratory. Both his daughters and their families moved to the United States, and he was also able to bring out his elderly mother and aunt. He became a naturalised United States citizen on 21 July 1941, so he was not an enemy alien when the United States declared war on Germany on 11 December 1941. His daughters still were, though, so they were restricted from travelling, and could not take care of their mother when she fell ill and died on 10 January 1942, although they were permitted to attend her funeral.

In February 1942, Arthur H. Compton established its Metallurgical Laboratory at the University of Chicago. As part of the Manhattan Project, its mission was to build nuclear reactors to create plutonium that would be used in atomic bombs. The Metallurgical Laboratory's Chemistry Division was initially headed by Frank Spedding, but he preferred hands on work to administration. Compton then turned to Franck, with some trepidation owing to his German background. Compton later wrote:

In addition to heading the Chemistry Division, Franck was also the chairman of the Metallurgical Laboratory's Committee on Political and Social Problems regarding the atomic bomb, which consisted of himself and Donald J. Hughes, J. J. Nickson, Eugene Rabinowitch, Glenn T. Seaborg, J. C. Stearns and Leó Szilárd. In 1945, Franck warned Henry A. Wallace of their fears that "mankind has learned to unleash atomic power without being ethically and politically prepared to use it wisely." The committee compiled what became known as the Franck Report. Finished on 11 June 1945, it recommended that the atomic bombs not be used on the Japanese cities without warning. In any event, the Interim Committee decided otherwise.

Franck married Hertha Sponer in a civil ceremony on 29 June 1946. In his post-war research, he continued to tackle the Problem of explaining the mechanism of photosynthesis. Meitner saw no break between his early and later work. She recalled that

In addition to the Nobel Prize. Franck was awarded the Max Planck Medal of the Deutsche Physikalische Gesellschaft in 1951 and the Rumford Medal of the American Academy of Arts and Sciences for his work on photosynthesis in 1955. He became an honorary citizen of Göttingen in 1953, and was elected a Foreign Member of the Royal Society (ForMemRS) in 1964. He died suddenly from a heart attack while visiting Göttingen on 21 May 1964, and was buried in Chicago with his first wife. In 1967, the University of Chicago named the James Franck Institute after him. A lunar crater has also been named in his honour. His papers are in the University of Chicago Library.

In his own research, Franck developed what became known as the Franck–Condon principle, a rule in spectroscopy and quantum chemistry that explains the intensity of vibronic transitions, simultaneous changes in electronic and vibrational Energy levels of a molecule due to the absorption or emission of a photon of the appropriate Energy. The principle states that during an electronic transition, a change from one vibrational Energy level to another will be more likely to happen if the two vibrational wave functions overlap more significantly. The principle has since been applied to a wide variety of related phenomena.