Don't
I really hate to pour cold water on the dreams of someone, especially when it comes to aviation, but here I must.
Don't do it. You are already well on your way of lining up the proverbial holes in the cheese that lead to becoming a statistic in the AAIB reports.
Here's why:
1) you are putting yourself under pressure. Setting a date which cannot be moved (birthday in your case) is always a bad idea when flying light a/c, no matter the airplane or your level of experience
2) you are contemplating a flight that - while possibly just about legal - operates right on the edge of the airplane's envelope
3) even if the wx cooperates (a big IF), then crossing the Channel on a hazy summer's day isn't quite the same as flying over the green fields of England. You can be in perfect VFR from a legal POV, but in reality be flying on instruments, as there is no discernible horizon. No big deal in itself, but another hole...
4) you are attempting all of the above with precious little experience
Take your GF flying around locally, same with her parents - separately. Thus you will also see how they react to being in a small a/c - not everyone loves it.
You will eventually fly to Le Touquet and hopefully far beyond. But take a little more time in getting there.