Thank you! I mistakenly assumed that this is order number because in this case it is the same for both sides. But it is rather exception than the rule - in most cases they are not the same. If it is a serial number, it has a very little value and probably even does not worth to be included in "other numbers".
While I typed it, I was getting doubts. I must have been told it, and it's true they are often close rather than the same on both sides. I'd like to find two copies of the same record to be absolutely sure.
I've seen Fonotipias that the artist has signed in the wax, but I can't remember if they were French. In my search for a copy of the same record with different serial numbers I came a cross a number 11 online.