I have at least an 80s(possibly older) frame that has horizontal dropouts, lugged steel with brazing and hooks for a frame pump. The previous owner repainted it somewhere along the way but chemical stripper took it down to a yellow original color but no decals or head decal. No serial that I could find either. The only identifier that I could find is a simple "B-M" embossed in the upper part of the head tube lug above where the head badge would be. Is this a custom build or something of a nature that would not inherently have a serial since there is no evidence of an erased serial?

most likely BCM for Bocama, not the frame builder but the lug brand...lots of builders/brands used BCM lugs.

So otherwise no chance of figuring who made it...

Pending pics, the absence of any brazed on fittings save pump hooks would suggest boom era or older. Serial numbers are not always in the traditonal, BB location. I've seen them stamped on dropouts, head lugs, seat lugs, brake bridges and just about any location of the seat tube.

The intial stage of investigation, besides the serial number and posting pics, would be to check the rear droput spacing, BB thread standard, required seat post diameter and checking for markings on the fork's steerer tube. They can often provide clues to the era, nationality and level, if not the actual manufacturer.

It has "Solida" cranks, cottered type. SunTour downtube shifters with a clamp on mount which also has a rest for the clamp brazed on the frame. Cables housings have stops for routing. I checked after chem stripping under every visible location to find a mark. The fork has a word printed on it but it did not strike me as a brand. It has similar crown lugging to some 70s/80s schwinns. Tomorrow I might get some pics, but for now the garage is cold and I don't feel like going out to it lol.

Reads French so far.

Take a good caliper to the stem as it enters the fork and measure that in metric.

The stem actually does say "made in France"

without those pix, we are just stabbing in the dark...so, since I like stabbing as much as anyone, here's a blind stab: Gitane.
It's French, there were many with BCM lugs and were a popular brand so a "high percentage" guess.