Literally translated as, having the peach, avoir la pêche means being in high spirits, having a lot of energy, feeling great physically and/or mentally — in other words, feeling peachy! It is an informal expression that is only used in casual conversation, but is not vulgar.
This expression appeared in the sixties: it may have evolved from the word pêche (peach) as slang for the face or head, or, according to this source, from the fact that it is also slang for a punch: a boxer who "has the peach” would then be a boxer who packs a punch, and therefore has a good, winning energy.
You may also encounter these related idioms: avoir la patate (having the potato), avoir la frite (having the French fry), avoir la banane (having the banana, probably because it evokes the shape of a big smile).
Eh ben dis-donc, tu as la pêche, ce matin !
Well, you certainly are in high spirits this morning!
The core of the expression is the peach, which gives way to variations such as: – Ça me donne la pêche (it gives me the peach), when something causes one to feel great, – Je n’ai pas la pêche (I don’t have the peach), when one is feeling down, – the adjective pêchu(e) (~peachy), a neologism that has yet to achieve dictionary status, and qualifies someone or something that has good energy, such as une chanson pêchue, a catchy, happy song.