candidature vs candidacy

candidature and candidacy both are nouns.

Word	Noun	Adjective	Verb	Adverb
candidature	Yes	No	No	No
candidacy	Yes	No	No	No

As nouns, candidature and candidacy are synonyms defined as:

Other synonyms of candidature include campaigning, electioneering, political campaign.

candidature (noun)	candidacy (noun)
the campaign of a candidate to be elected	the campaign of a candidate to be elected