Why do people from different countries look different?

If you're assuming that variations in genes cause most of the differences that seem to give Americans, Frenchies, Spaniards, Russians and others their characteristic looks, you're probably wrong. Our geographic boundaries have not been around long enough for gene selection to do the job. But think about language. Different languages (even dialects) require speakers to develop, to position, and to strengthen certain facial muscles at the expense of others. These facial variations enable a wide variety of physical types to "look" French or Latin (etc.), and contribute a lion's share to "national" appearance.
Here's a simple experiment. You can speak French with a better accent, more clearly and rapidly, if you extrude your lips slightly while you talk. Try it, messieurs et Mesdames! And look at pictures of the French, who often have those extruded lips.