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No, freedom of speech doesn’t protect you against false statements. There’s literally a ton of other laws that penalize that, depending on the context. Purgery, slander, libel, breach of contract, just to name a few.
I already said that there were limitations to free speech earlier. But untruth is also protected under the US Constitution. It all relates to a possibility of harm.
If i said that I was the Easter Bunny, it would be a lie, but who is harmed by it?
If I falsely yell fire in a crowded theatre and people get trampled, then harm, or a risk of harm is evident.
These are all standard arguments on free speech. But, yes, there are many carve outs where an untrue statement is protected under law. I just don’t have the time or inclination to list them all. You can check them out yourself.