Ah, found another data point in WOTC's "Rules of the Game: Familiars" article (emphasis mine):
A familiar has an Intelligence score of at least 6, or higher if the master's level is 3rd or higher, as shown on page 53 of the Player's Handbook. The threshold for humanlike intelligence is 3 (see page 9 in the Player's Handbook), so a familiar is as smart as a person, but not necessarily as smart as a brilliant person or even an average person. A familiar's minimum Intelligence score of 6 makes it smart enough to understand at least one language, usually Common (though it doesn't gain the power of speech until the master reaches 5th level). This allows the familiar to respond to fairly elaborate commands and undertake fairly complex tasks. As rule of thumb, a 1st-level master's familiar is capable of doing anything a preadolescent human child can do. As the master's level increases, so does the familiar's ability to follow orders and perform tasks.
A familiar does not learn new languages as its Intelligence increases along with its master's level.
A familiar uses its own Intelligence score if it is higher than what its master's level allows. A familiar can benefit from spells and effects that boost Intelligence, such as the fox's cunning spell. As with any temporary Intelligence increase, the Intelligence enhancement does not give the familiar any extra skill points or languages, but the familiar uses its new, higher, Intelligence modifier for Intelligence checks and Intelligence-based skill checks.
So the familiar is smart enough to know "at least one language" but doesn't learn more just by getting smarter. There's no guidance or reasoning re: why "usually Common," though it's probably just because all of the core PC races automatically speak Common. I'd be inclined to say a familiar should at least understand the language the master usually speaks - for most PCs in most campaigns, that is "usually Common."
But that still doesn't address how/when the familiar can understand other languages the master knows.