Something rampant is uncontrollable, though in heraldry it means something on its hind legs, such as a Lion Rampant, rearing up, as opposed to couchant, lying down for instance. The heraldric sense has existed since the 14th Century in English, while the rampage sense has only existed since the 17th Century.
The word has its origins in French, ramper, meaning to ‘creep’ or ‘climb. The –ant suffix of rampant is derived from French too, and is a common way of creating an adjective from a noun. Examples include: bouyant, flippant, coolant, lubricant, propellant, Protestant, triumphant, depressant, compliant and accountant.
Related to rampant is ramp, now meaning a slope, this sense of the word only originated in the 18th Century. In Middle English ‘ramp’ meant to ‘rear up’.
Unrelated to rampant is rampart, which is descended from a separate French word, remparer, meaning ‘to fortify’, from re- and emparer, meaning to take possession of, and that from the Latin ante- and parare, meaning to prepare.
The Old French ramper derives not from Latin, like much of French, but in fact from Frankish (*rampōn meaning to hook, or climb), and so ramper is actually Germanic in origin. The Frankish is descended from the Proto-Germanic *hrempaną (to curve, shrivel).
An interesting related word is ripple. Ripple is an alternative form of the Old English rimple, which was descended from the same Germanic root meaning ‘to curve’.