Fruit descends from the latin fructus, meaning ‘enjoyment of produce’, from the verb frui ‘to enjoy’. Besides the edible sense fructus also carries a sense of monetary value, and so it is also the origin on the word frugal.
Frui is the infinitive of fruor, I enjoy. Fruor resembles a latin passive verb, but is active in meaning. Verbs like this are uncommon in latin, but do exist, and are called deponent verbs. Other examples include conor or morior, meaning ‘to try’ and ‘to die’.
Fruor is itself descended from the proto-indo-european *bʰruHg-, meaning to have enjoyment of or make use of. It also gives the latin word frux meaning supplies or fruit, as well ultimately as the French frugalité.