Yes, but the Right has that majority in the senate, and already refused a similar proposition in september.

They might still let it go through though, as the french public is really really not divided on the subject.
As the article states, a recent poll found that 80% of the voters want better protections for the right to abortion (and in the remaining 20% you're bound to have a lot who don't think it needs more protection because they think the current law is good enough, but are pro-right to abortion).

Outside of Integrist Catholics / TradCaths circles, there's not really any debate on abortion in France. The Far Right don't like it but they don't have the political drive to attack it, it would be a political self-inflicted wound for them.