Uni Exchange 'aupairs' are a totally different kettle of fish IMO. I have a nearby university that is always on the lookout for host families. If I was approached by the uni to take on a student who would 'remunerate' me in kind (ie childcare and housework), rather than cash, then of course it goes without saying that this student must be allowed to attend all the classes they need as that is the main reason why they are in the country to begin with.
As the risk of generalisation, I do think French aupairs' English tends to be on the poorer side and I can understand their need for intensive lessons. But as a host family, my need is for good English and hence I would never take on a uni exchange English course 'aupair'.
There is a suitable family for every aupair. I take it upon myself as my responsibility in loco parentis to ensure that our profiles match as much as possible. Not all aupairs require English lessons and if they do, not want to do or afford intensive private lessons.
Anna, if aupair rights arise by contract, I agree rights can arise verbally, not just in writing. Even if the aupair mentioned she would be taking english lessons, I would also have told her what the working hours are (specifically a 3 pm pickup). So unless all the details are hammered out in advance (which it cannot as I have explained re: ESOL courses), there is a grey area contractually if the aupair wants everyday classes that interfere with the 3 pm pickup. In practice, I specifically query my potential aupairs about whether they want english language courses, explain the estimated cost and time commitment of ESOL classes and how to get to them, the difference from private classes and how they are going to fund the classes. This way I avoid any misunderstadings.