My car renault clio 1998 keeps stopping?

my car is a renault cilo 1998 nov, just the past few weeks its playing up in that it's cutting out when its waiting at lights etc, plus now is cutting cut when driving. I changed the battery in the key but not to sure what is wrong. Iam really worried that it will happen and someone will go in the back of me. Also did get it checked out and it did not cut out for the three days someone was looking at it. Please help thanks,