Kinda, sorta, ...
Aside from the Orleans, a subbranch of the Bourbons, there were (and are) still members of the Bourbon family to this day, even under that name.
The main line of the Bourbons died out in 1883, but there's still lots of descendants from Philip V, Louis XIV's grandson who became king of Spain. Supporters of the Orleans claim that they are excluded from the succession to the French throne by the fact that Philip V assumed the Spanish throne, this renunciation of being codified by the treaties of Utrecht. This would mean that succession would devolve upon the next (and only other surviving) branch of the Capetian dynasty, the Orleans. However, a small portion of monarchists (who assumed the name of "legitimists") believe that such a renunciation would be contrary to the French fundamental laws and therefore support the heads of these branches.
During and after the First World War, their claimant was none other than the carlist pretender to the Spanish throne, don Jaime de Borbón, duque de Madrid aka "Jacques Ier, roi de France et de Navarre". He himself was mainly interested in his Spanish heritage, but he did assume the title of "duke of Anjou" (after the courtesy title of Philip V before he became Spanish king) and handed out the occasional French dynastic order.
However, this legitimism was a minority current without any political leverage. Which is testified by the fact that, while the Orleans and Bonaparte claimants were banned from entering French soil between 1886 en 1950, the French republican authorities didn't deem it necessary to apply this law to don Jaime, who died in his Paris appartment in the avenue Hoche in 1931.
Nowadays, I've got the impression that - at least among hardcore monarchists - the legitimists faction (now represented by noone other than the great-grandson of Francisco Franco) has overtaken the Orleans one in numbers. In part due to the controversies surrounding the Orleans family, partially because the older line is no longer handicapped by also being Spanish claimants, but I guess also due to the fact that monarchism has become so irrelevant that those remaining might as well support the most extremist theory.