There is now an electronic version for which INPI provides an electronic fingerprint (hash) and stores the original file (in the owner's account). This is better described at the French-language link below. Casual inspection did not reveal a public proof checking facility, something that is in fact provided by the company MaPreuve, for example. MaPreuve requires a Java application, which none of the browsers on this computer wanted to load, but this would be a really useful service. Storing the original document electronically, in my view, detracts from the value of the INPI service and I would have been happier if they had just stored the electronic fingerprint.
Set up of electronic Soleau Envelope – https://www.ipside.com/content/set-electronic-soleau-envelope
e-Soleau – https://www.inpi.fr/fr/services-et-prestations/e-soleau
MaPreuve Proof verification service – https://www.mapreuve.com/en/verifier-une-preuve.php