Thank you for your question. Unfortunately, there is no official service to notify someone of a death, nor of the filing of a death certificate. You have to organize this yourself, either by making local acquaintances, or by setting up "alerte de deces" on private websites. The second option is very easy, just follow the "alerte deces" links in the following websites: http://www.dansnoscoeurs.fr/alertes-deces ; http://www.ouest-france.fr/obseques/alertes/ . Another way, if you do not want to register, is to make constant online searches, and on the two mentioned site, to which you can also add this one, which does not offer the alert service: https://www.simplifia.fr/avis-de-deces/
Once you have found an obituary, use the information there to request an official death certificate. That can be done for free by anyone on the following link: https://mdel.mon.service-public.fr/mademarchev5/sfjsp?interviewID=etatCivil
Once you have the certificate, you can deal with the estate. Regarding the notary, the problem is you might have to go back to the same one, or one nearby. This is because in France, notaries have exclusive geographical competence for estates in their area, and sometimes there is just one notary per area. Therefore, you may wish to have an English-speaking local attorney with you, or just a translator, but you might not be able to avoid the notary.
I hope my answer was useful and look forward to your rating, which is essential to my activity.
Dr I L Vlad