In France, you can't do a paternity test on your own even if you're ready to pay by yourself, the only way to be able to do so is if there is a legal procedure ongoing (mostly if the mother wants to make the father pay and he refuse to recognize the kid).

The reasons are to respect privacy and to protect the kid : the judge can refuse a father's demand to run a paternity test on a kid because it would mean the dad might stop raising the kid with his mom, hence they consider it detrimental for the kid's life.

I find it so unfair to men that unlike women we deny them the right to be 100% sure their kids are their owns. If I happen to have a kid someday, I'd certainly prefer my partner doing a paternity test and be reassured and fully invested in raising our kids if he has even a slightly unfounded doubt, because you can never know and trust someone fully sometimes, especially if you're the anxious type.

So instead of allowing that my country prefers to protect cheaters and not put them in front of the consequences of their actions. Like, it's not like the kid wouldn't have any father in the end, he always have one. If it's unfair for the child it's also unfair for the man who have been lied to for years and that can't get those years back.