Not many people might actually be inclined to ask this question, or it may be an assumption that the Buddha spoke one or both of the ancient Indian languages Pali or Sanskrit.

In any case, the answer is no, the Buddha did not speak Pali. He likely spoke a mixture of now-lost local dialects, as he was remarkably well-travelled for his time.

... the actual language of the Buddha and origins of Pāli are unknown, [but] the existence of Pāli literatures in which the words of The Buddha and his immediate disciples were enshrined is of immense value to the students of Buddhist philosophy, psychology, ... and so forth.

Per the Pali glossary entry (emphasis and cross-linking my own):