For we believers there can only be one answer. Before the Tower of Babel all of mankind spoke the same tongue, the universal language: Esperanto.
Spencer Wells did a study on this exact issue. I would be inclined to say that the first language probably wasn't a human language. Humans(Homo-Sapiens) are not the first sentient race. Neanderthal, our cousins, spoke advanced languages long before humans even existed. And even before then a common ancestor existed between Neanderthal and humans that likely spoke a complicated language.
The first language to have been spoken by a human would probably be lost in time today, but when it existed it would have been spoken somewhere in Central Africa. Spencer Wells thinks he found a tribe in Africa that speaks a language similar to that of the language spoken by our ancestors. I'd give him a look on Youtube if you want an in depth look on this topic (:
The first language was Hebrew. It was in its original form, the language that Adam spoke in the garden of Eden. For this reason it could be referred to as man’s language. It was the language spoken in Noah’s day, though with a growing vocabulary. In still further expanded form, it was the basic language that survived when God confused mankind’s speech at the Tower of Babel. (Gen. 11:1, 7-9)
Since Hebrew appears to have been the language employed by Noah's family, and- as AnnNettie pointed out- survived the Babylonian confusion, then that is the likely candidate.
Shem- the son of Noah- and his family is reported to have continued on in his father's language, which appears to be Hebrew. While those in the Mesopotamian region, were scattered by the sudden introduction of various "sets" of tongues.