Saint-Jean

With the verbs venir and tenir and their derivatives, the -ien- sequence comes about as a result of stem change: the e in venir becomes ie when the stress falls on that syllable. So you get je viens and il vient but nous venons (without the stem change). The -ien- sequence isn't an ending and has nothing to do with the third person ending. So you have two present-tense stems for venir : vien- (for all singular and the third person plural) and ven- for the nous and vous forms. The endings are -s, -s, -t, -ons, -ez, -ent.

The third person ending in -ent is a relic of Latin and was never pronounced in French as far as I know. The difference between is best illustrated with ils viennent, where the -ent ending is silent, but the stem vowel is -ien and gets pronounced.

The silent e (e caduc) is pronounced in traditional poetry and song, as it was once pronounced in speech. In the case of peuvent and aiment, the vowel isn't nasal, despite an n being written, so aime and aiment should be pronounced the same.