In the capital, French will definitely get you further than Dutch. Most people who don't have dutch or french as their native language speak french so it is mostly used as the default language if you are unsure. Of course, it really depends on where you are. Also, I hate to generalize but most native dutch speakers know at least some basic French while the reverse is not always the case. As far as jobs go, it varies widely, there are quite some jobs available where English is the main language, as well as many primary dutch/french speaking companies. Only real constraint I can think of is if you look for a job where you need to speak a lot to customers (sales person, working in a bar, etc.) french will probably be a requirement (dutch not necessarily).
As far as just living there and talking to people and doing grocery shopping: Belgians speak English quite well, we are all taught English at school and we don't dub English television, so it gets you far, I think about the same as in Sweden.