I will explain.

What is a paternity test: A man now may know if a child is his son (=from his lineage) or another by doing dna test with 2 samples: 1 fragment from him and 1 of the (presumed) son, which go to laboratory. It is called a paternity test.

Just a bit of context. "Historically, men could not always tell a son was theirs." This assumption is FALSE. They often could tell he was not:
Because they knew if they saw the woman at the time of the conception. Because they knew when some phenotypics charasteristics COULD NOT be theirs. Same is for aborption. Assumption that women always may abort is FALSE. Women most of time just didnt have the knowledge to.

Here is the real reason to interdiction of paternity test in France: MOST OF FRENCH WOMEN ARE UNFAITHFUL (Yes, look at the statistics). HENCE the opposition to this test (while it is authorized in all other countries) on the grounds of: -the integrity of the body (while medically assisted procreation is authorized...) - That blood ties are not this important (while biology says the opposite with microchimeras) - That a man can very well raise another's child (while a man marries to have a child from him precisely)

https://masculinites.fr/discriminationsparentalite/inegalites-dans-la-loi/un-enfant-qui-nest-pas-le-sien/