DH teaches a fair few children already bilingual in French or Spanish. Generally they either stay in the lesson, but do separate work, or they go and work with one of the other language teachers in another classroom, if the other language teacher is not teaching.
It also depends what year they enter at. So if they come in later they may do the same work, as bilingual students are still entered for GCSE etc and have to learn the methods and requirements. If they come in at year 7, they are prepped to take the GCSE in either year 7 or 8, and then they start working on AS level stuff (this is in a school that only goes up to Year 11, so takes quite a bit of extra work from the teachers, but they do sort it).
However, in the case of one or two, if they come in fluent in French/Spanish, but not speaking much English, then they have English lessons instead, still often with a free MFL teacher. Obviously this wont apply for the bilingual students, they just do different work.
Quite commonly they find that while the child speaks and understands fluently their reading and, especially, writing are not a high enough standard for even GCSE sometimes, in which cases they do the relevant parts of the lesson and not others.
One bilingual child at dh's school (which I also teach at, hence knowing the results, 'tis not big-mouthed dh) unfortunately only got a D on his GCSE because he refused to believe that his reading and writing wasn't good enough and wouldn't work on it. Despite his mother telling him that she couldn't understand when he wrote.
Quick overview, but hth.