No. A mediator is neutral and impartial, helping each participant express their needs and build an agreement, but providing legal advice to neither. Each can consult their chosen lawyer, in France or the other country, before, during and after mediation.
When I conduct mediation, I never become a participant’s lawyer during or afterwards. Conversely, if I act as your lawyer, I may suggest mediation, but another mediator conducts it.
At the information meeting, I explain the respective roles of mediator and lawyers.