You should definitely assume that any application you make to the firm will then be known about throughout the whole business. Consultancies have good communication lines across offices when it comes to recruitment. They want to be sure that if a candidate really messed up at interviews with one office, they do not then get hired through the back door by another of their offices.
Having said this, it can be worth applying to more than one office in certain circumstances - since different offices have different recruitment needs. I would do this sequentially though - so apply to your preferred office first and then to subsequent offices thereafter. If the London office is looking for people with certain skills and you don't have those, you could find you are not offered an interview - but then the Paris office could have different requirements and so you do get an interview there. Because you never actually failed any interviews in London this will not count against you when your CV is being screened by Paris.
Hope that makes sense and good luck. Tony
