In English, the full legal term appears to be "assault and battery" or "affray and battery". The corresponding term in French would seem to be "coups et blessures".

TechDico

coups et blessures assault and battery – law – iate.europa.eu

[photograph 2012.201.b0924.0555]… Caption: "Frontier City’s "Doc Holliday" and "Marshal" Clay were free on $500 bond each Wednesday after they pleaded innocent to charges of aggravated assault and battery, which grew out of the "arrest" and pistol whipping of two teenaged boys at the tourist attraction in OKC…
general – core.ac.uk –

However, it is asserted in this article from the Wikipédia that the criminal code in Switzerland and Canada uses in fact "lésions corporelles".

Nevertheless, in France the legal term is "coups et blessures".

(FrWiki) Les coups et blessures sont une notion de droit pénal.
(user LPH’s translation: "Coups et blessures" is a notion of criminal law.)

There appears to be no synonym in the domain of the law, in France.

Lésions corporelles is not a criminal offence as such, it is used in medical descriptions and helps determine how to define a criminal offence. Battery is a criminal offence.
The first terms that comes to my mind for lésions corporelles is "bodily harm" or "physical injuries"¹.

I am not a lawyer so I might be wrong, but I assumed that battery did not necessarily imply bodily harm to a person. It might also be defined differently in the US and in Britain (or other English speaking countries).

In France I know the terms :

Voie de fait which doesn’t imply corporal injury.

Coups et blessures which implies corporal injury and is sometimes translated into English as "physical assault and battery" and as Körperverletzung in German.

There might be others. You can also look at this page (issued by a commercial firm) which provides a list of legal terms with their correspondence in French and Am. English.

^{1 Körperverletzung auf Deutsch.
2 Also keine Körperverletzung.}