"he is known for defeating the Gauls"
victoriā belli gallici praeclarus est
Clarus or praeclarus are the way to go, especially in a good sense. There are a zillion examples. Notus is really still only the participle of nosco, without the connotation of to be known for.
An ablative is the most common case, but other constructions exist: e.g. genitive: T. Livius, eloquentiae ac fidei praeclarus in primis, (Tac. A. 4, 34); or in + Abl. multi praeclari in philosophiā et nobiles, (Cic. de Or. 1, 11, 46)
As for translating “for defeating the Gauls” with victoriā belli gallici, it is a matter of taste. Latin privileges nomina actionis in such constructions, and e.g. Suetonius wrote in victoriā belli civilis (Suet. Caes. 75), “when he won the civil war.”
Famōsus is also an option, also with ablative, but it is used much more in a bad sense (infamous) than in a good one. In present-day Italian it’s only used in a good sense, and it’s a famosus false friend.