Carcavi was born in Lyon, the son of Jean de Carcavi, receiver-general of the districts of Languedoc, Guyenne, and Lyonnais. There are no records of university education, but evidently he studied law and early on acquired a strong interest in mathematics. In 1632, through the help of his father, he was made conseiller to the Parlement of Toulouse, where he first met Pierre de Fermat. They remained close friends throughout their lives, and Fermat later sent him copies of his mathematical texts. Carcavi was encouraged by Fermat to write to other mathematicians such as Descartes, Roberval, and Torricelli, and he later developed an extensive correspondence network. In 1636, with money from his father, he bought the office of conseiller to the Grand Conseil and moved to Paris.

Paris provided Carcavi with a fertile intellectual environment. He developed close ties to Roberval, as well as to Mersenne and the young Blaise Pascal, and later became a member of the Académie de Montmor. In 1648 his career suffered a temporary setback, when financial difficulties of his father forced him to sell his position at the Grand Conseil. For a while he traded books before entering the service of Duc de Liancourt. Through a stroke of luck, another of Roger du Plessis's protégés, the Abbé Amable de Bourzéis, introduced him to Colbert who was seeking someone to catalog Cardinal Mazarin's library. After thus demonstrating his aptitude, Carcavi was appointed custodian of the Royal Library by Colbert in 1663. He held this post for twenty years and played a decisive role in enriching the library's holdings.

Carcavi's relations to Descartes were seldom straightforward. After the death of Mersenne in 1648, he offered his extensive correspondence to Descartes. The following year, Carcavi informed Descartes of Roberval's objections to his Geometry. Descartes replied with a refutation of his claims. When Carcavi publicly defended Roberval, Descartes severed all ties with him. He died in Paris April 1684.

See also Geometry; Mersenne, Marin; Roberval, Gilles Personne de