I live in Northern California, I pay family support to my ex but is it the same than spouse+child support?
How can I stop paying alimony to my ex who's getting married?

I have never heard of "family support." Usually, child support and alimony are two different things. As for the remarriage of your ex, file a motion with the court that issued the original order to advise them that your ex is getting remarried and ask the court to terminate the alimony order. Your ex's remarriage should release you from the obligatio of alimony. You'll still have to continue paying child support but you should no longer have to pay alimony.

How long was it ordered to continue for or what were the exact terms for the family support ordered? Check to see if there is anything in your order about any amounts being "allocated" within the total "family support" amount.

Alimony is usually ordered to continue only for half the length of the marriage. It can be different if it was a long term marriage. And child support until the child turns 18 or until graduation if the child is a full time student and living at home, emancipates, or gets married.