Skintones look OK to me, not exactly THAT much redder than the old DVD. The transfer on the French BD is an unmitigated DNR nuked disaster.
EDIT: Just looked at the DVDBeaver BD/DVD comparison and it looks like it's another compromised DVDBeaver comparison taken in the wrong color space and thus introducing a claret red skin tone. Total amateurs the people who contribute to that site, which has the sheer audacity to now put their faulty screenshots behind a paywall!
Just to explain without getting too techincal, certain software that you can use to take Bluray screenshots with - like VirtualDub, which I strongly suspect DVDBeaver grabbers like to use - will only output/save screenshots in rec.701. What this means is that the saved screenshots have incorrect colours, the most noticeable problem being that something that is a light red will look more like a claret shade. This could be what is making the screenshots look so bad in the DVDBeaver screenshots. It's possible that the Blu-ray transfer is just inconsistent, but DVDBeaver have a looooong history of taken screenshots in the wrong colour space.