Best advice i can give you on this one, try find a decently fast car, doesnt have the be the fastests.
Just one that accelerates ok.
Turn on the speedlimiter and just follow him, cause hes max travel speed is the same as yours with the limit on.
If you bump into something, turn the limit off, get back in range and turn it back on.
Should be pretty easy that way, i had my troubles aswell on this one when i tried it the first time, but the speed limiter helps alot.
Oh and another thing, stay off the handbrake in follow missions.
Its more a pain than good really.
Just break with the down arrow or S or what ever.
Hope this helps a bit.
Thanks for the advice. I actually did all that and it worked. I finished the game a few days ago.