Hi,
I'm not an instructor or anything like that, but I obtained the swiss license not too long ago. Yes, as far as I know if you are swiss citizen you have to obtain a swiss license. I also did my AFF in the US and didn't have any problems in getting it accepted over here. After AFF you have to perform several thematic coach jumps similar to the american system, however in Switzerland each topic is concluded by an exam (e.g. aerobatic figures, tracking etc.). Once you completed all the jumps required and passed all the exams you are eligible to take the final exam, which consists of two self-spotted accuracy jumps and a RW jump with one instructor. Of you also have to pass a theoretical exam. It usually takes around 50 jumps to obtain the license, but that also depends how fast you progress since there is no strict jump number requirement.
Here you should find all information: https://docs.google.com/file/d/0B77akVj-zZhzZlVkWkN4OFV3dk0/edit (since you mentioned you lived at the french border, I assume you are french speaking ;-))
P.S.: I never heard of anybody having problems getting their license accepted outside of Switzerland.