I participate heavily in French Language & Usage, and have used many other foreign language sites on SE, and I personally don't like using the International Keyboard option Windows has because it's quite troublesome for me.
It would be profoundly helpful to me, and probably to many other casual visitors who aren't necessarily deep enough into their studies to have an international keyboard enabled, if there was a little panel with the set of accent marks used by that site's language.
I took the liberty of making a simple mock-up in MS Paint using the question I was in the middle of asking on FL&U. Notice the little bar of special characters next to the input field. The little arrow at the bottom was meant to indicate that you can scroll down to view more.
This is not for sites like Chinese, Japanese, Korean, or Russian, which use entirely separate characters. For those it would not be as feasible nor as helpful. Only for sites that use the Latin alphabet with small alterations, like French, Spanish, Polish, and Portuguese.