Hi, Horbat:
1) I agree with Looby re. the birth certificate and baptismal records for your mother. Make sure you have the long-form birth record (if one is available in France). She might have been baptized by her mother in France; she might also have been baptized in England by her mother and stepfather after they were married. One or all of these records might name your mother's biological father.
Here's an example from my own life. When I purchased my grandmother's long-form birth record from the US (I'm in Canada), to my surprise I learned that she had been born at a Salvation Army Maternity Home! This took me down a long, interesting path with some surprising results and a fairly solid theory as to her father's identity. This was before DNA testing was widely available; I'm guessing now it would probably either provide me with more corroboration for my theory or disprove it altogether.
2) Also per Looby, make sure you have a copy of your mother's mother's full marriage record, in case it might offer any clues. Depending on the timing of the marriage, the record might list your mother's stepfather's regiment and rank.
3) Keep in mind that not all records from the First World War have survived. Knowing where your mother's stepfather was from, and which regiment he might have served with, should allow you to ascertain whether or not the records should even exist, assuming he did serve. If the individual records no longer exist, the regiment's diaries might still be around, and they might sometimes offer information about the dates and places where a regiment was active. (For example, this is the case for the Cheshire Regiment in which my husband's grandfather served.)
4) Sometimes individual soldiers were named in brief newspaper reports on new recruits for the town/city; it wouldn't hurt to search the online newspaper archives for your mother's stepfather's name during the right time frame; even his first initial + last name might provide you with a clue to help you get going in the right direction. (If he had siblings that might have served, you could also search for their names, in case that might provide a clue.)
5) The same might be true with a newspaper notice of the marriage.
6) If there was a gap between the time of your mother's birth and the time of her mother's marriage, try to find out if there might have been any claims against the biological father for child support (in case he was still alive).
7) Find out if your mother might have been officially adopted by her stepfather.
Good luck in your search!
Regards,
Josephine
