the President's wife, Carla Bruni

This page is 6-10 years' old. That should raise alarm bells.

https://www.service-public.fr/particuliers/vosdroits/F14042

According to this governmental website, in France, paternity tests can be done, though only (1) in the context of judicial proceedings (e.g. spanorce case where the man claims he is not the father of his children; single mother claiming so-and-so is the father of her child; etc.), and (2) if the alleged father consents to being tested.

Basically, you can't buy DIY paternity home kits.
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When you have nothing to say, quote yourself ~ Solfadore

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