The origins of the humble frog remain somewhat unkown, even today.
English, being multiple languages in a trench coat, can have its roots stem from anywhere. The Old English frogga "frog",
or a short form of many other variatons (ex: frose, forsc, frox) are possible sources. It can even be considered to be from the German word for frog
Frosch, due to English being a Germanic language.
Other languages note the frog's actions, such as the hop or the croak. Sanskrit's provate "hops", or Russian's prygat "to hop, jump",
and Latin's rana (imitative of the frog's distinctive croaking sound) are examples of this phenomenon.
Intriguingly, it was a British derogatory term for "Frenchman" in 1778. This was because the French were stereotypically thought of as eating frogs. Though prior to this, it
was meant to refer to the Dutch, where 'frog-land' meant 'marshy-land', indicative of a Dutchmen's origins.
Sources can be found at this link, as well as this one.