How can I find out if a close encounter in flight would be classed as an airprox?
I've finally identified the flight you most likely saw out of the window. There was an oddity with Fligtradar24 where the data was missing for the flight, but I've straightened out that mystery. 

First for the Flightradar24 oddity:
You were on B757 registration G-LSAE on from LBA to PMI. The previous flight that aircraft had taken was LS444/EXS4CX from HER to LBA. For some reason when your flight left LBA it was still showing on FR24 as LS444/EXS4CX. After it crossed into France over Le Havre it changed to showing as LS831/EXS81WF which is usually a flight from MAN to PMI. I can't explain this, but the registration, time and route matches exactly with the routing shown for LS257 on FlightAware, so this is your aircraft.

Now for the flight you saw: 
There were only two RyanAir flights that you crossed paths with that might have been close enough to see. FR6462/RYR88FJ passed about 15-20 miles from you. But at 6:39 UTC over Lunay, a RyanAir B737, flight FR9052/RYR43EZ passed very close. I'm sure this is the aircraft you saw. According to the data, your aircraft was at 35,000 feet on a heading of 164° feet and the RyanAir was at 36,000 feet on a 12° heading. So, although the lateral separation was very close, the standard vertical separation of 1,000 feet was maintained.