As far as I can tell the tartan he's wearing is the Duke of Rothesay Hunting.
Actually, I think it's the Prince of Wales hunting tartan, because there is no alternation between a single thin white line and three white lines from sett to sett.
As far as I know, anyone can wear Rothesay or Prince of Wales.
Actually France has quite a few princes - The Comte de Paris is the Chef de la maison d'Orleans, and would be king in an Orleanist revivial - he has three sons the Daupin (Duc d'Vendôme), the Comte de Clermont and the Duc d'Angouglême. All of these would be "princes du sang royal."
There is also the Spanish claimant to the French throne, Louis Alfonso, Duc d'Anjou et de Bourbon, Chef de la Maison de France who would be Louis XX. His younger brother Francis (Francisco) would be a "Prince du sang royal."
The French just don't recognize their royalty any more.
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