Thanks Mel,
Afraid that I've not had much free time today to look at your Parasol. Immediate impression was of a Morane-Saulnier of some kind, but now I don't think it can be a M-S as closer inspection reveals N type struts and cabanes (although I haven't trawled all of them), but the "house-style" doesn't fit, but is it French?
How many seats, it looks like there are two foot-boards so a trainer maybe?
Is there a radial lurking in the silhouette?