Is cheek kissing common in the US?

I am French and I was told American people usually just say hi, shake hands or sometimes hug if they know well each others.

This is correct. Americans rarely initiate cheek kissing.

If you initiate a cheek kiss, and the kiss-receiver understands what you're doing, they will probably reciprocate and think, "Oh, how charming and foreign!"

From Wikipedia:

According to the March 8, 2004 edition of Time Magazine, "a single [kiss] is [an] acceptable [greeting] in the United States, but it's mostly a big-city phenomenon

The Wall Street Journal points out how it's affecting business, and when to do this.

Chicago Tribune has a piece on how it's spreading, and notes that it's not just a case of "is it in America now?" but that it's cultural, and different regions make sounds when they do it, might do one kiss or two, and it varies even in the same city.

Having traveled around there, I can confirm that one of my friends did it but perhaps because she has a lot of Latin American friends, and she points out that some of her friends were taken aback when she did it in Florida. So short answer - it depends. I'd watch the person you're greeting - if they go in for it, follow their lead, until you feel comfortable with what to expect.

I grew up in Texas and I have always observed it to be very common for family and close friends to cheek kiss when they greet one another, especially in a home or holiday setting. When we were young it was mostly the adults and little kids, but it has become more common all around. However, some people find it an odd invasion of their personal space (family or otherwise).

I have noticed that it is becoming more common here among young people in big cities (especially between my friends who have lived/traveled abroad), but still seems to be between close friends.

Even my Latino friends here in Texas seem to follow the same cultural norms. Ie. Sometimes in public - nearly always at home/special occasion.

Well I spent 6 months in the USA in 2014 and as a Turk, I can say that cheek kissing is highly common in Turkey. So I faced a little trouble at the beginning because American people that I meet during the 6 months were like just saying hi, not kiss or hug. If you meet someone on the street they do not even stop to talk a little, just say hi, and go on. In Turkey we stop and talk for more than 20-30 minutes which is something I do not approve :) But just hi is not enough for me I think.