Ménage and manège are often confused but we have it from an authoritative source – a planning inspector dealing with an appeal concerning a site in Hertfordshire (DCS Number 400-028-935) – that if it’s horse-related it’s likely to be manège. Here is what he says in a Procedural Matter paragraph:-
The decision notice, case officer report, application form and application planning statement all use the word ‘ménage’ whereas the appeal statement refers to the word ‘manège’. The Oxford English Dictionary uses the latter for its description of an enclosed space for the training of horses and the practice of horsemanship. I have therefore proceeded on the same basis throughout this decision, and replaced the word ‘ménage’ where previously used.
There are appeal examples relating to manèges at 23.2332 of DCP Online.