Well as they both want to become muslims they should first convert then get married (islamic aqd nikah/marriage). And everything is fine.
As the major problem from a shari'a point of view is that they might live together in sin! We could discuss the matter if a civil solidarity pact is equal to 'aqd an-Nikah but if it's not regarded as the same in France then it won't be accepted. If it's equal still one must ask a Scholar if this would be accepted to be a 'aqd an-Nikah for non-muslims which will mean they keep their "mariage". therefore a 'aqd an-Nikah or an islamic marriage would be the best to clear away all these doubts!
They can't live together as cohabitants if they are muslims. So these steps are necessary!
If they don't get married like this they will be doing a big sin.
For more Details see
What to do after converting to Islam while happily married to a non-Muslim husband?
Will a (non-Muslim) marriage still be valid if the husband or the wife reverts to Islam?
And Allah knows best