I don't think that's quite accurate. Dutch is not closer to English than French. The reason why we generally are better at English is because our language footprint is so small. Other than the Dutch (from the Netherlands), nobody in Europe speaks Dutch. Movies get subtitled, not overdubbed, simply because the market is too small. Most movies/series on TV are in English, so ever since we are small, we are exposed to the English language much more. In Wallonia and other French speaking parts, they simply get the French overdubbed movies and series. It's mainly a question of economics. It wasn't worth the trouble to hire actors to dub every movie and serie on TV, because Netherlands+Flanders is simply too small.
Furthermore, due to the same reason (small market), there is less money to make original content in our own language, and again our TV networks are forced to buy (mainly English) content to show on TV. The main exception has usually been childrens movies (like Disney etc).
Wallonia also gets a plethora of talkshows from French networks, but also a lot of other cultural influences, like French music. For us, considering the Netherlands is a much smaller country than France, that also is much less so.
And, when we visit another country, people there don't speak Dutch. They usually understand English or French. So the French speaking part, needs to resort to another language far less yet again, than Dutch speakers.