Seems like Mark Stevens is a marque specialist for Gillot. He's on Classic lightweights and the V-CC. Worth finding out all you can. I wonder if it was used for grass track, mass start or time trials?
Cyclocross? With track ends? Not a lot of CX around when this was built. Probably a 'road/path' frame for TT'ing and general fixed wheel club riding, maybe some grass track racing. Whatever, nice find, lucky you!
I can post you a can of elbow grease works great on both on bikes and floors .I have some left.
Spent 3 hrs on a very wet Monday cleaning carpets around the home ....loads of brownie points
Enjoy the project . Looking forward to the build thread .