As you state, some Belgians are overly sensitive to language issues. Usually, as a tourist you should not have problems due to that, but of course you can always get unlucky and meet the exceptional sour grape.
Brussels is officially bilingual (Dutch-French), but in reality French is the dominant language. It is also an international city, so English (and a lot of other languages) are common. In parts of the town where you encounter a lot of tourists both languages should be equally fine. Both will be understood and a lot of languages are used. If you go to the less touristy parts, French will be your best bet. You simply are less sure that English will be understood and from your accent it will probably be rather clear that you are a native English speaker. Whoever you are talking to will probably switch if they think English would work better.
If you would travel to Flanders (the Dutch speaking northern half), English is your best bet. Simply because people, especially younger ones, are usually more fluent in English than in French. I fail to see who you are helping by speaking French.
In Wallonia (the southern French speaking half), I would start in French. Knowledge of English is rather bad, even though it is improving among the younger population. The same argument about switching to English as I described for Brussels is valid.
Source: I am Flemish (native Dutch speaking), working in Brussels. In Brussels I will often address unknown people in French. So I would definitely not be insulted if someone addressed me in French.