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.

As it is to change the constitution, it's a little more complicated than a simple majority :

The text need a simple majority in the national assembly AND a simple majority in the senate (which is not the case for regular laws).

Once you have that, there is 2 way for it to finally happened :

• The congress (National Assembly + Senate) is united in one assembly (it happens in Versailles traditionally) and 60% (3/5) must vote for it to pass.
• A National referendum is called and then it become a simple majority referendum.

And that is without talking about the Article 11 of the French 5th Republic Constitution that is, risky to say the least.