Is he who mocked a child delivering a sermon and quoting verses from the Holy Quran an infidel, and what should he do?

What you mentioned does not necessitate disbelief or mockery of the religion. Mocking the speaker does not mean mocking the religion. The default is that a Muslim remains a Muslim, and a Muslim is not excommunicated for ambiguous words or actions. If there is even one way to keep a Muslim within the fold of Islam, then it should be acted upon.