My OED leads me to suppose that the route from Latin via French is the obvious one, linked clearly to penitent. But funnily enough J, it seems there was a form of word very close to pent that got superceded by penitent:

[a. OF. pénitent (14th c. in Littré), ad. L. pænitent-em, pr. pple. of pænitere (pœn-, pèn-) to repent; this as a learned form, in ecclesiastical use, gradually displaced the popular OF. peneant, -ant, and ME. Penant. In pænitere and its derivatives, the original L. form is held to have been with pæ-, but in med.L. pœ- was usual; in Romanic pe-.] [e.a.]

By the way, I noticed another few little sprigs of interest in looking at the whole collection of words from pent to paint:
Latin used re~ before vowels and red~ before consonants (for the general sense of ‘back’ or ‘again’) – one of the few examples in English of the latter form is the timely conjunction for penitent: redeem.
Pent is also an obsolete or dialect form of ‘paint’, as well as the clutch of meanings to do with pressure and constraint.
Pent is also closely associated with bent, sharing the pressure sense.
Paint is also an archaic nautical back formation, so sailors beware of being asked to paint the anchor! trans. To make fast (an anchor) on a ship with a ‘painter’.

So under pressure of time I shall slope off (he notes for our resident French speakers!) and repent me of my sins of omission (he reflects), leaving you with a reminder of John Keats to explore if the fancy takes you, that almost seems to fit the ecclesiastical mood.

To one who has been long in city pent,
'Tis very sweet to look into the fair
And open face of heaven,--to breathe a prayer
Full in the smile of the blue firmament.