That's Broca's area. Mirror neurons may indeed play an important part in second language acquisition. Mirror neurons are supposed to be all about observation and imitation. Interhemispheric foreign language learning
"There is much current debate about the existence of mirror neurons in humans. To identify mirror neurons in the inferior frontal gyrus (IFG) of humans, we used a repetition suppression paradigm while measuring neural activity with functional magnetic resonance imaging. Subjects either executed or observed a series of actions. Here we show that in the IFG, responses were suppressed both when an executed action was followed by the same rather than a different observed action and when an observed action was followed by the same rather than a different executed action. This pattern of responses is consistent with that predicted by mirror neurons and is evidence of mirror neurons in the human IFG. 10.1523/JNEUROSCI.2668-09.2009"
First Evidence Found of Mirror Neuron’s Role in Language
"...the findings suggest that mirror neurons play a key role in the mental "re-enactment" of actions when linguistic descriptions of those actions are conceptually processed."