Few data are available on La Grange's life, except that he entered the Oratory in 1660 and left in 1680 to become a parish priest in Chartres. During these two decades, he taught philosophy at Montbrison and Le Mans and theology at Troyes.

La Grange is the author of a two-volume treatise The Principles of Philosophy against the New Philosophers. Although these “new philosophers” include Pierre Gassendi and Emmanuel Maignan, La Grange's main target is Cartesianism. The title polemically alludes to Descartes’ own Principles of Philosophy. La Grange also aims at Descartes’ followers, Rohault mainly, and, unnamed, Malebranche, whose theory of the “vision in God” is denounced (1675–79, 1:78).

La Grange's preface refers to Louis XIV's 1671 decree, which banned the teaching of Cartesianism on the ground that it jeopardizes the traditional account of “the mysteries of the faith.” Similarly, La Grange's first and main reproach is that the principles of Cartesianism are incompatible with a number of revealed truths. According to him, theological dogmas provide a litmus test for philosophical principles. Even if these principles appear to be evident and certain, they cannot be but false if they generate conclusions that are opposed to revealed truths.

In particular, contrary to Descartes’ claim, it is impossible to account for transubstantiation without the tools of “ordinary philosophy,” such as accidental forms. As a consequence, La Grange undertakes to rehabilitate real qualities, that is, entities which are ontologically different from the substance in which they inhere, instead of being just modes of that substance (see quality, real). Thence, La Grange tries to prove that accidents are not reducible to their substances. This applies to qualities residing in the soul, such as virtue or knowledge as well as to physical properties. The latter are not reducible to relations between parts of matter, that is, to figure and motion, as the Cartesians want it. Thus, La Grange directly challenges Cartesian natural philosophy and contends that no serious theory can do away with entities such as quantity (which entails that extension is not merely the essence of bodies), heat, sound, and colors.