The British probably smell bad because of the notariously awful British food. (Food can have a major effect on how one smells.)
The rest of Europe, I don't know about (never been there), but I know that many/most Europeans don't have the daily-shower fetish displayed by most Americans. The German exchange students we had at our high school all smelled somewhat of sweat - almost as if they didn't even use deoderant. And, as you said, the French use less soap than just about anyone else in Europe. (I don't know if there would be accurate statistics from many of the Eastern European countries.)