Answer:
Part 1). Yes, Alex be better off in Paris if the relative prices between American and French meals (p_a/p_f) are lower in Paris than Austin because his capability to buying goods growths so his cash is fundamentally value more locally.
Part 2) No, Alex be better off in Paris if the relative prices between American and French meals (p_a/p_f) are higher in Paris than Austin because even though he can buying the same components, they will cost extra, and he will consume less goods than living in Austin