My imperfect understanding is that Muslims believe Jesus was a prophet of God, who was sentenced to crucifixion. But then he was miraculously rescued, and someone (perhaps Judas) was miraculously put on the cross in his place.
That's my understanding, anyway.
Also, from what I've read, the idea that Jesus never existed is a theory that was popular a long time ago, but no longer considered very credible. The Jewish/Roman historian Josephus wrote of Jesus, I thought Tacitus did as well.