You've done well! It looks in pretty good condition and apart from the handlebars and saddle (should have drop bars), it appears to be pretty much standard.
I reckon you're probably right that it's about 1980 (you can tell from the stamping on the bottom bracket shell - I'd need to dig out the details to tell you exactly how). It's definitely a fairly high end frame, and it might even be a very late PX (a PXN10, which was about the last). If so, that's good news as the PXs are worth money! Can you give a few more details: what's the make of the chainset (I think Stronglight), brakes (Mafac sidepulls?) etc? and the number on the BB, and exactly what sort of Reynolds transfers are they - just green, or green with the 531 in red and red lettering saying 'ultra legere' ? Does it say '3 tubes renforcés' or '5 tubes renforcés'. Is it five or six speed?
Please, don't 'upgrade' it - get some proper period bars, levers and saddle, and keep it standard.