I’m not too much into his history but how much inbreeding was going on then? Like the Tsar’s of Russia? Hemophilia in there perhaps?
However, these conditions are NOT autosomal recessives which have a better chance to express themselves in a smaller population where there are fewer marriage choices.
The other big thing was the French nobility, in general, made valiant, though not always successful efforts to marry no closer than four degrees of consanguinity away. This was pretty much the case with other ruling families.
There were also NEW HIRES (as we might call them) who married in. Christopher Columbus married a Braganza Princess (for example).
That's roughly like having Princess Ann of England marry a chauffeur.
No, there was no inbreeding. That came several centuries later.