I see and hear this phrase a lot.

Problem:
The adjective creates a redundancy.

Explanation:
The noun “gift” in this phrase means a thing or experience voluntarily given without any kind of reciprocal payment required or expected.

So the adjective “free” creates a redundancy when combined with the noun “gift”.

For fun, I searched Google for “free gift” (with the quotation marks, to avoid variations) and got about 9,110,000 matches.

Not all of these matches were what I was seeking. For example, Google returned “Free Gift-Giving Labels”, but this does not agree with the sense of the phrase “Free Gift”.

However, I am sure that many millions of the returned matches did agree with the sense of the phrase, which obviously makes this phrase a common English blunder.

Solution:
“Gift”