Will a Carte de Séjour issued in France allow freedom of movement around other EU member States?

Here the existence or not of a deal has no impact on the outcome of the UK leaving the EU.
The Titre will – of itself – only allow visa free movement around the Schengen area and only under Schengen rules (i.e. 90 days out of every 180 days on a rolling period basis). 
In effect – bearing in mind that the EU currently proposes Visa free travel for up to 90 days in every 180 for British nationals in any event – there is no cross border freedom of movement benefit achieved by the French issued Titre de Séjour, irrespective of whether there is a deal or no deal. The only benefit of the deal is that Freedom of movement is maintained during the transition period as a result of the Withdrawal Agreement itself.