I re-watched the Minions film last night, and wondered about their language. The Minions are these chaps and their buddies (there are no female Minions, as far as I can tell):
They speak in a language that isn't quite understandable but you get the gist - like Pingu or the Clangers. However, unlike Pingu or the Clangers, there are very definitely words in the Minions' speech, and some of them are definitely recognisable. Some are English but most are Spanish or Italian, or a mix of them all. There's also a little bit of romance language grammar in there too: at one point, one of the Minions says me le due, meaning 'I will do it', and you can see the object clitic le (a clitic is basically a type of pronoun that goes before the verb in romance languages, like the m' in je m'appelle Laura).
When I asked about the Minion language on Twitter, @terminologia directed me to this Arika Okrent article which goes into much more detail, including noting the many aspects of 'baby talk' - in that me le due sentence, for instance, there is the object form me - just like an English toddler might say me do it. The article also points out that some of the language is Indonesian - I hadn't noticed it, but there's a very clear terima kasih 'thank you' at one point. (Actually, I thought terima kasih was Malay, and so it is, but it was borrowed into Indonesian and that's the language the director is familiar with.)
Here's the Minions Dictionary (though I don't think it's quite complete).