As far as I know French does not yet have a word for an air kiss. To find an equivalent one should know the difference between an "air kiss" and a "blown kiss" which the OP does not make. Both are symbolic gestures of kissing practises but involve different gestures and have different social and affective meanings.
Several definitions can be found on the web, I'll point to Wikipedia's.
A blown kiss (called flying kiss in India) is a kiss that is
"blown" to another by kissing the fingertips and then blowing the fingertips, pointing them in the direction of the recipient. This is used to convey affection, usually when parting or when the partners are physically distant but can view each other.
A blown kiss means you are not actually touching the person you are sending the kiss to, you kiss your hand and then the hand delivers the kiss to the wind that carries it to the recipient. It is an affectionate gesture often associated with departures, you do not blow a kiss when meeting.
Elle baissa la vitre du compartiment et se pencha pour lui envoyer un baiser de la main dans le bruit de la locomotive qui commençait à démarrer. (Gare du Nord 193X) 1
The air kiss is a pretence of kissing: the lips are pursed as if kissing, but without actually touching the other person's body. Sometimes, the air kiss includes touching cheek-to-cheek.
When giving an air kiss you are close to the other person, you might even be touching them, and you kiss them without your lips actually touching the other person. You do not entrust the kiss to your hand but you actually kiss the air. That's why it is called an air kiss.
An air kiss is not meant to actually reach the other person, there is no feeling in it, it is a greeting gesture, and not usually a departing gesture.
An air kiss is a hallmark of contemporary showbiz society, especially of female American celebrities.
Well, not only female. Here's one air-kiss that made the headlines earlier on this year, with a video that is an excellent explanation of how to air-kiss: Donald Trump, Mike Pence and the air kiss heard round the world.2
What could we use in French to reflect a kiss that is given not out of affection for the other person but just for the sake of the paparazzi around?
What comes to my mind in the case of political people is donner l'accolade which contains the physical closeness with hands and cheeks but no actual kiss delivered onto the cheeks. Searching for an illustration of donner l'accolade here's what I found:
Ivanka Trump, fille de Donald Trump donne une accolade au colistier de son père Mike Pence. ;
The picture is definitely that of an air kiss.
But the phrase might not always be very satisfactory in the case of actors and showbiz people in general.
Un baiser hollywoodien, although fake, is definitely not that. 3
Un baiser de star, I do not like it either, I still prefer donner l'accolade although it sounds a little weird in some contexts.
After giving it much thought and not finding anything better when donner l'accolade seems out of place, I'd suggest falling back to plain old embrasser. Etymologically embrasser means holding in your arms and does not necessarily imply any actual touching of the lips on any part of the body, which is what an air kiss does.
It really made my day when I met Hillary and she gave me an air kiss.
Which I would translate as:
Ce fut le jour de ma vie quand j'ai rencontré Hillary et qu'elle m'a embrassée.
She pulled down the window of the carriage and leaned over to blow him a kiss while the engine was pulling out of the station. Free translation. Wink to Papa Poule.
This is an example chosen only for language purposes only.
Un baiser hollywoodien