Can I set a different preferred language per site?

Is there a way to change the preferred language in the browser (Firefox and/or Chrome) based on the visited site?

Most of the time I want websites to be displayed in English, but when I visit a French site that has an English version, it displays the English version, even though I'd prefer to see it in French (since I'm French).

Is there an extension that would let me control that setting on a per-site basis?

On Firefox, you can use the lightweight Quick Accept-Language Switcher extension and change the locale every time you access that site. You need to do that manually but that's the easiest and safest way I've found to do that today. There was another extension (Quick Locale Switcher) that did remember site-specific locale settings, but users have reported that it doesn't work anymore.

You can also look up an extension that lets you modify HTTP headers for specific sites, and use it to change just the Accept-Language parameter. Requestly for Chrome seems to be a good choice, but I haven't tested it.