Yes, we use 'Assaut' here in the UK as 'Assault' means to commit a common attack on someone who is an unwilling opponent.
We usually explain to people that 'Assaut' refers to a 'controlled contact' contest, with all malice and power removed from the blows - as in regular sparring in class, or a 'friendly exchange' of technique.
When we speak of 'Combat' we simply explain it as a 'full-contact' competition.
As far as 'Integrale' is concerned, there really is no obvious translation. They are really a kind of 'Unitard' (which no one in the UK really understands anyway), an all-in-one body-suit or, perhaps, a Licra Girlie Thingy!
I think to translate Assaut to Assault would be a bit problematic... as it is a technical word for a type of criminal offence in the UK. We tend to say Assaut ourselves
Hello Charlemont, Pas mal ta traduc sur le topic Combat & Assaut training - j'ai beaucoup aimé!
I use an internet site to help me translate, it does the basic work then you only have to correct things: SYSTRAN language translation technologies. I think other people will have their own favourite sites to give you. I have started to keep my own Savate dictionary. I had a job finding out INTEGRALE in English, don't really know how to say FORFAIT either. Luckily, Pugil is lots of help. How would you translate ASSAUT ? Is Assault a fit word?
Hello I am French teacher of French Savate and I seek English discussions on the French Savate . I need some to validate my file for the Patent of State 2° degree.
Some of the things poking out of the integrals seem less than girlie... But then, how would I know? 
