That doesn't make any sense: "French men often circumvent these laws by sending samples of DNA to foreign laboratories". Did you mean foreign labs lobbying in France?
The "labs lobbying" comment was kind of tongue-in-cheek: making fun of the "crazies" being paranoid about "crazy feminists"...
The real reason's probably more about bioethics: no dna profiling of people who don't consent without a court order (and children being too young to consent, you need a court order for a paternity test).