He was born in New York City to an American mother from Boston and a French-Italian Father. He was raised in Florence, Italy and in 1917 he was sent as a boarder to Bedford Modern School in England leaving in 1924 to study architecture in London. After also graduating from the Royal School of Architecture in Rome, Girard refined his skills in both Florence and New York.

In 1952, Alexander Girard was hired to head the fabric and textile division. Girard worked with George Nelson and Charles and Ray Eames to form a design team that has influenced the fundamentals of design throughout the United States and the rest of the world. Girard initially established a fabric collection based on his architectural training. His first fabric line consisted of plain upholsteries and geometric drapery prints—stripes, circles, and triangles. He went on to create many more patterns and designs, largely inspired by folk art. He also worked with a 19th-century textile mill he discovered in central Mexico, to create a line of handwoven 100% cotton fabrics. Because of the excellent quality and array of colors available, he developed a range of colorful “mexidots”and “mexistripes” which he used in many of his projects including installation backing, ground for environmental enrichment panels and upholstery.

In 1956, Just Lunning, President of Georg Jensen, commissioned Girard to design seven table settings for an exhibition on 5th Avenue in New York. Each setting was created around a vignette outlining the personalities and situations of the company at the particular table. He created place mats and dishes specific to the project.

In 1960 Girard designed every aspect of the 'La Fonda del Sol' restaurant located in the Time-Life building in Manhattan, New York. in a Latin American and contemporary theme/style, including menus, matchbooks, tableware and the ceramic tiles on the floors and walls. Girard created over eighty different sun motifs found throughout the restaurant.

In 1962, Girard and his wife established the Girard Foundation in Santa Fe to manage their art collection that numbered over 100,000 pieces, including toys, dolls, icons, and other ethnic expressions. Girard's design work was heavily influenced by his passion for folk art. In 1978, Girard contributed his immense collection to the Museum of International Folk Art in Santa Fe, New Mexico, United States. The museum opened to the public in 1953 and has gained national and international recognition as home to the world’s largest collection of folk art.

In May, 1965, Girard began his design work for Braniff International Airways re-branding campaign called “The End of the Plain Plane”. This project gave Girard the opportunity to work with textiles, color, and graphics on a grand scale, redesigning everything from the sugar packets to the ticket counters to the color of the planes themselves. He used colors like light and dark blue, beige, ochre, orange, turquoise, and lemon yellow to make the planes recognizable from the ground. Italian couturier fashion designer Emilio Pucci designed attendant uniforms.

Girard was also commissioned by Brody to design the L'Etoile Restaurant (1966) in the Sherry Netherlands Hotel, New York, a French restaurant with austere decor featuring a range of silver and greys featuring glass engraved with the names of French luminaries and daisy shaped tables in the bar. The Compound Restaurant (1967), in Santa Fe, New Mexico, is in a clean modern yet traditional New Mexican style with inlaid Mexicotton ceiling tiles and nichos featuring a mix of folk art and Girard’s own designs.

Girard also designed a line of furniture for Braniff's ticket offices and customer lounges. This furniture was also available to the public by Herman Miller in 1967 but was available for one year only.

The Girard Wing houses the popular permanent exhibition, Multiple Visions: A Common Bond, which showcases folk art, popular art, toys and textiles from more than 100 nations. Opening in 1982, this unorthodox and delightful exhibition was designed and installed by Girard, and remains popular with the public.

This Herman Miller showplace was a unique space filled with textiles and folk art pieces on Manhattan’s East 53rd street. Textiles and Objects was an innovation demonstrating textiles as an integral part of interior displays for both designers and the individual consumer. The showroom also featured folk art Girard collected from around the world. T&O closed in shortly after opening, due to insufficient marketing and a public was not quite ready to add such colorful and exotic objects to the typical 1950’s palette of their homes.