In Brussels, both Dutch and French are considered the main languages. Logically, it should be about 50/50. However, Brussels Airport is located in Zaventem, which is not in Brussels, but in the Flemish (Dutch-speaking) area (Flanders). So the chance of finding native Dutch-speaking staff should be higher. (again, in theory, as I don't know the staff).
Last time I went, staff spoke Dutch to each other as well.
Staff there also certainly speak at least basic English.
I'd speak Dutch by default in Brussels airport, but really it depends on which language you are more comfortable with talking. If you doubt, you can always ask them before you start the conversation. I'm sure they'll appreciate it.
If you're talking about check-in service, it might depend on your airline, though. I remember China Airlines staff at the check-in mostly spoke Chinese and English one time. This is not the case for airport staff.