For our purchase in France we used the same Notaire as the sellers with no problems. However we have heard stories about a local Notaire not doing his job properly by ignoring items like cars from an estate which has caused huge problems later down the line when the inheritor wanted to sell the car ( as it should have been shared with her brother).
A French friend inherited her parents house along with her brothers. One brother took all the money, he was friends with the Notaire and she is having to take him to court to recover her share. Another British friend who had a house in France ( full resident under Article 50) went back to the UK to die. Her children were cut out of the inheritance all bar one daughter. Long and ugly story, thé Notaire was appointed by the imoblier and was acting for both the buyer and seller. She insisted that all the children were reserved inheritors. However another Notaire was appointed and was adamant that as nobody in the family was an EU resident at the time of her death then her Uk will applied and it could all go to one child. It took the new Notaire to have to threaten to take the old one to Notaire tribunal before she backed down and returned most of the 500 euros we had paid upfront.
So our experience is there are good ones and some very bad ones, you have to be on top of the case yourselves.
Regards
Nick