Ailes de Pigeon is when "the dancer performs a Cabriole Devant, then the legs change and beat again, then change once more before the dancer lands on the leg he or she jumped from, leaving the other leg extended in the air. Also known as 'Pistolet'."
Wow, that's a mouthful! I have never heard of this move before, and so needed to look further. The Oxford Dictionary of Dance by Debra Craine and Judith MacKrell states that Ailes de Pigeon is "A particularly demanding ballet step which most famously occurs in the Blue Bird variation in Sleeping Beauty." When searching for this section of Sleeping Beauty, I believe I found something close to what an Ailes de Pigeon is, but all the landings aren't what is described in the Ballet Dictionaries. The one's that I found either land in Fifth Position or Sur le Cou-de-pied.
The two most notable ones that I found are from The Royal Ballet (1963) and Dutch National Ballet (???). Both times this move is performed by the Cavalier in a diagonal crossing.
Ultimately, this move remains a mystery to me, and I might have to do some asking around to learn more about it.