The letter, which told ministers "the language of the Republic is French," came after Cabinet members used the title "Silver Economy" for a new economic initiative, The Local.fr reported Wednesday.
"Our language is able to express every contemporary reality, and describe innovations that are constantly being born in the areas of science and technology," Ayrault wrote in the April 25 letter.
Ayrault wrote French had been "inscribed in the constitution of 1992" as "the language of administration, and of the courts."
Arnaud Montebourg, minister for industrial renewal, and Michele Delaunay, junior minister for the elderly, announced April 24 they were planning to group businesses related to the elderly into a sector of the French economy to be called the "Silver Economy."
"The English term seems to us most appropriate for a sector planning to expand exports," an adviser told French daily Le Figaro.