Once you have struck a verbal deal, you should confirm your offer in writing (and in French):
Specifying all details of both sellers and buyers: names (individual or SCI), DOBs, registered adresses, etc.;
Describing precisely the property, (with the plot number as indicated in the land registry);
Detailing the agreed price and timeframe for completion;
Without forgetting any conditions that you wish to include in the compromis, and any details agreed with the vendor.
When that letter is counter-signed by the seller, you have the essence of the deal.
That letter should be presented to the notaire, who will make it happen. Don't wait to get in touch with a notaire - because until the compromis is signed and 10 days have elapsed, your purchase is not guaranteed.