Cost sharing is according to the local CAA rules, optionally over-ridden by the local airspace rules.
The UK CAA allows cost sharing in a G-reg, by way of an exemption to a general ban on any payment to a PPL pilot. This exemption is valid worldwide, so (assuming say France does not object) you can cost share your G-reg all the way across France.
The FAA allows cost sharing too, but the UK CAA prohibits all payments to the pilot of a foreign reg plane (ref ANO article 140) without DfT permission - which you won't get anyway. This makes the FAA cost sharing scheme illegal in the UK so if I (being N-reg) take a passenger up I make it clear they cannot contribute anything.
In practice, of course, you will never get caught doing illegal cost sharing. Until there is an accident, when the passenger(s) are quite likely to spill the beans if they can get a bigger payout in return
