In Le Bourgeois Gentilhomme (1670) Molière has the Maître de philosophie say:

Et l’R, en portant le bout de la langue jusqu’au haut du palais; de sorte qu’étant frôlée par l’air qui sort avec force, elle lui cède, et revient toujours au même endroit, faisant une manière de tremblement, RRA. (Acte II, Scène IV)

which is the apical trill that is supposed to still represesent the Latin pronunciation.
At the end of the 17th century this apical trill started being replaced by an uvular [ʁ]. This was a fashion that started at court and spread in Paris and fashionable society.

The present standard guttural /r/ (pronounced as a voiced [ʁ] or voiceless uvular fricative [χ]) appeared between the end of the 18th c. and the beginning of the 19th c., it spread from Paris to the towns and then to the rural areas.

Urban legend has it (so not to be found in academic works) that this guttural /r/ started at the court of Louis XVI because he could not pronounce the normal, rolled r and to flatter him the court adopted his uvular pronunciation.

Note that in some parts of France the alveolar trill is still common, in the south east non urban areas. I think it’s still common in Québec.

Sources :

• Petite histoire de r from Le cabinet des curiosités.

• Histoire d’une langue, le français (Marcel Cohen, éditions sociales, 1973)