The translation of "À la semaine prochaine" is "See you next week". Semaine is "week" and prochaine is "next". So it means that "À la" means "See you". I have not come across any definition that shows "À la" to mean "See You". Is this one of those sentences that just have to be memorised and word by word translation should be ignored.
"See" translation is voir. Shouldn't the translation be "Je vois semaine prochaine"