Which one is correct "I have a lot of free time." OR "I have much free time." [closed]

"Much" in this sense is not incorrect but is now old fashioned. It was perfectly standard in the 17th century as can be seen from Luke 10:40 in the King James translation of the Christian Bible which starts

But Martha was cumbered about much serving

This Ngram suggests that "much work" was the normal way of saying the opposite of what you quote until about 1870, that "a lot of work" started to be more common then, overtook "much work" from around 1965 onwards and is now about three times more common.

I have used "much work" and "a lot of work" in the Ngram analysis because I believe that "free time" is a more modern concept and would give a less clear indication of the relative use of "much" and "a lot of" in this type of context. Interestingly the Ngram results are a fairly close match to my personal opinion of the change that I have observed in my lifetime.

"I have a lot of free time" seems to be the correct one here. Not a native speaker, but "I have much free time" doesn't sound right as an affirmative sentence, though this isn't perhaps grammatically incorrect.