Rime riche
Rime riche is a form of rhyme with three identical sounds (phoneme) including the stressed vowel. In classical French poetry rhymes normally have to be visual too: both sound and spelling have to be identical.
In French poetry, rhymes are usually classified on the basis of the number of rhyming sounds. A "rime pauvre" includes one common sound at the end of the two rhyming segments. Consonant sounds do not rhyme on their own and so a "rime pauvre" must be a vocalic sound. 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.
A "rime suffisante" includes two identical sounds, one of which must be a vowel. Two consecutive vowel sounds being extremely rare in French, "rimes suffisantes" are usually in the vowel-consonant or consonant-vowel format. In the following example of "rime suffisante" by Racine in Britannicus, /ne/ are the two rhyming sounds, identically spelt "-nés".
Au joug depuis longtemps, ils se sont façonnés;
Ils adorent la main qui les tient enchaînés.
A "rime riche" includes three identical sounds. In the following example of "rime riche" by Racine in Phèdre, /aʃ
Ce n'est plus une ardeur dans mes veines cachée,
C'est Vénus tout entière à sa proie attachée.
There is no canonical name for rhymes over three identical sounds. They are frowned upon in classical French poetry.