Fucking up is locking your keys in the house, forgetting to put the bins out, losing your phone/laptop/wallet.
Fucking up is NOT taking some woman's number.
Or worse actually using it to text her! FFS!
You won't trust him again.
He doesn't deserve your trust. How long have you been with him?
Bin him.
If you end this relationship over this you will show him that you won't tolerate cheating, in any form.
It may be that he truly regrets it and works day and night to win you back. Good.
It may be he does all the above and you don't want him back. Up to you. He's still going to learn a lesson not to cheat.
If you allow him to whine, simper, cry and beg for a few days, then forget/forgive all about it, then all he's going to have to do is whine and simper until you stfu and get over it.
Either way, binning is the only way forward. Any other way exposes you to letting him get away with it and do it to you again.