beau geste vs gesture

beau geste and gesture both are nouns.

Word	Noun	Adjective	Verb	Adverb
beau geste	Yes	No	No	No
gesture	Yes	No	Yes	No

As nouns, gesture is a hypernym of beau geste; that is, gesture is a word with a broader meaning than beau geste:

beau geste (noun)	gesture (noun)
a gracious (but usually meaningless) gesture	motion of hands or body to emphasize or help to express a thought or feeling
	something done as an indication of intention
	the use of movements (especially of the hands) to communicate familiar or prearranged signals

beau geste (verb)	gesture (verb)
	show, express or direct through movement