I'm French and will travel the 14th of June to the US. My ESTA expires the 14th of June 2013 and I'm wondering if my ESTA will be valid when I'll land in the US on the 14th of June 2013.
Does someone know anything about that?
You have an edge case. Typically, it is OK for the ESTA to expire during your visit. From US Customs and Border Protection website:
You should either contact the nearest USA consulate and get a definitive on if it is considered valid for the day of expiration or not or, as most ESTA applications are approved within minutes, you could simply renew your ESTA. An ESTA may be renewed prior to the previous one expiring.
On the renewal front a little Googling turned up:
On UsaEmbassy.gov. That is 3 days, so you are just about on the right side of the equation, depending on when your flight is. Most likely, since you already had an ESTA, you'll be approved automatically in minutes.