Samirlsn
Just a quick thought - do you have a JAR PPL or a FAA PPL?
If it's FAA, you cannot leave British airspace in a G-Reg plane and you would need to access an N tail nunber (you probably have this figured out already.)
Hope this helps.
BTW, I 'did' my first channel crossing during my PPL and then solo at about 70hrs.
Like a lot of things, what sounds a bit intimidating is pretty straightforward when you watched someone else show you how.
France isn't your only option either, Ostend is a fun airport with a 3200m runway and some good restaurants a cab ride away.
Plus the Belgiums are very, very nice - I work with a business school in Brussels and spend a lot of time across there ..... the ATC people reflect the national stereotypes of being relaxed and friendly - but they are also professional.
Good luck