Rime riche (French pronunciation: [ʁim ʁiʃ]) is a form of rhyme with three identical sounds (phoneme) including the stressed vowel.
In classical French poetry (between Malherbe and Romanticism) rhymes normally have to be visual too: both sound and spelling have to be identical.
In the following example of "rime pauvre" by Racine in Andromaque, the rhyming sound is /y/; identically spelt "-ue": (...) ma vengeance est perdue, s'il ignore en mourant que c'est moi qui le tue.
Two consecutive vowel sounds being extremely rare in French, "rimes suffisantes" are usually in the vowel-consonant or consonant-vowel format.
Ce n'est plus une ardeur dans mes veines cachée, C'est Vénus tout entière à sa proie attachée.