There is, due to a lack of translation, an inclination to think of Common as English - and given that it is a 'common' language, chances are it's as much of a mutt as English is. Assuming it wasn't simply created by humans - making it actually 'Human' by the language-naming-traditions we seem to follow - it's an amalgamation of the other commonly spoken tongues. Or, at least, that would make some sense.
On the other hand, there's no linguistic spillover. There aren't elven phrases which sound a lot like their Common equivalents. Generally speaking, 'ale' in dwarven sounds much different from 'ale' in common. Pretty much the only word that's the same in all languages is 'Al'noth' - and given that it's an elven word, one wonders why that has perpetuated so long. Not everyone who uses magic likes elves after all.
This could well be a reason that many people are trying to learn Elven though. If elves have so great an understanding of magic that their word has become the iconic one for 'the magical energy field around Layonara', chances are that many arcanists would learn Elven just to understand the reference manuals in the Great Library, or wherever.