You're probably already on to this, but just in case:
If you are doing measurements or distance calculations with GPS readings, DON'T get caught up in all the precise spherical trigonometric maths and formulas. It will send you bonkers.
Over "small" areas, eg, within 100 km, the errors are small enough to ignore, eg, if you are telling your students how far they are from the starting point, and they are a kilometre away, does it really matter if that distance is off by a metre or two eg 0.1% ?
Each degree of latitude is 10000000 metres / 90 degrees = 111111 metres (as measured by you French from north pole to equator through Paris, I think ;-).
Each degree of longitude is that same 111111 metres multiplied x Cos(degrees latitude from equator) because they get smaller as you get closer to the north pole.
So to calculate straight-line distance, you can convert degrees to metres, and then use Pythagoras. Remember that the metres-per-degree conversion factors are different for latitude (constant, doesn't change) and longitude (gets smaller as latitude increases).
If you want to be slightly more accurate, you can use the average degrees-latitude-from-equator that spans the area you're calculating across, instead of using the degrees-latitude-from-equator of your current location.