Vocal Alteration is a 1st level arcane spell that changes a creature's voice. Its a transmutation, not an illusion; it actually changes the voice to something else. Per the spell:
The target can vary the disguised voice just as it could its normal voice. For example, a halfling female given a male dwarf noble’s voice and accent could speak in falsetto, with a rural halfling accent, and so on.
Now if you have a familiar you can target it with a spell regardless of it's Type; by this rule you can cast Enlarge Person on a familiar despite the fact that the creature is a Magical Beast. Combining that ability with this spell, could you change your familiar so it could speak common? It has an Int of 6 right at the start which gives it access to a single language; you could select Common and then cast this spell to alter it's voice to actually speak if that's legal.
The spell changes your speech. It does not give you speech.
If the familiar can speak, then you can change that. Some (Parrot, Raven, Thrush) get the supernatural ability at 1st level, all get speak w/master at level 5 and gain speak w/own kind at level 7. The familiar rules does not mention them gaining any languages. Where do you get your info that states otherwise?
If you give them a magic item with an int bonus, they get a language from that. If you give them a magic item with language skill(s), they get a language from that.
/cevah