What languages are spoken by Muslims?

Prophet Muhammad (saw) spoke Arabic.

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Arabic
Muhammad (PBUH) spoke in Arabic, one which differs slightly from the modern Arabic spoken today.
The Prophet Muhammad spoke Fus'ha Arabic, which is the type of Arabic that the Qur'an is written in.

Weather or not the above answer is true or false doesn't matter because whatever language Muhammad (PBUH) spoke wasn't what Jibril (Gabriel) spoke because Muhammad (PBUH) was unlearned in the language of The Holy Qur'an.
Prophet Mohammed (peace upon him) spoke Arabic.