A Latin form *volĕre would have been stressed on the first syllable. Italian volere is stressed on the penultimate syllable, like a Latin form *volēre. There could have been a Vulgar Latin form *volĕre that was later replaced with voˈl[e]re, but it seems more parsimonious to just give *volēre as the ancestor of the Italian and French forms.
"The Destiny Of Latin Second Conjugation Infinitives In Romance", by S. Davis and Donna Jo Napoli, goes through the etymology of the Italian verbs whose infinitives end in -ere with penultimate stress. According to Davis and Napoli, there are only 22 such verbs.
18 are from verbs with attested Latin infinitive forms in -ēre.
2 are from verbs with attested Latin infinitive forms in -ĕre: saˈpere vs. Latin sapĕre and caˈdere vs. Latin cadĕre. Sapio is an -io verb in Latin, but cado isn't.
2 are from verbs with Latin infinitives not ending in -re: poˈtere vs. Latin posse and voˈlere vs. Latin velle
The root vol- does fit the phonological criteria that Davis and Napoli identify as relevant for the shift of cadere and sapere from the root-stressed to the theme-stressed category.