(Not sure if this is the case I was thinking of, but it popped up with a minute's searching: https://nationalpost.com/news/world/texas-man-ordered-to-pay... )
What's unusual (and newsworthy) in that specific case is that the child was a teenager by the time the paternity test happened, and Texas law doesn't remove any child support obligations imposed prior to the test. I believe that man was still contesting the outcome.
If anything, this is a great example of how important paternity tests can be. And why the U.S. should not outlaw paternity tests.
https://lawandcrime.com/video/man-legally-forced-to-pay-chil...
https://5newsonline.com/2017/01/12/oklahoma-man-ordered-to-p...
I'm not a lawyer, but my understanding is that this law inhibits laboratories outside of France in doing business in France.
And DNA testing seems too easy to me to be prohibited. We shed DNA all the time and it is becoming easier and easier to run PCRs or even sequence genomes.
Of course, the legal issue is with the invasion of privacy, and potential harm to the children's psyche, so there is actually some justification.
What about the potential harm to the psyche of a husband who doesn't know if he is the father of some children?
Children are generally granted more protections. Not sure how to complain about that without sounding weak and immature.
On the other hand, if you're going to extract payment, you should probably have to provide evidence that payment is due.
Felony paternity testing...I have no words.