how to move object while following spline path?

example video

Hi. I'm trying to do make run game like video up there.

My goal is my character will be running on curved roads and roads will pre-set up pass by specific points. user only can controll left and right direction. character will run forward automatically with following road line.

First I had tried to use curved shader, and it was not fit with my goal. It was for infinite run, infinite world.

so I thought I need to make roads that pass by specific points.

So I made roads with spline curve. And Now I can make follow the spline curve to my character.

But problem is I have no idea how to move my character while it is following spline curve. I wanna move my character left or right on roads like that video.

Is there any idea to move object while it is running on spline curve? Or is it wrong to use spline path to this? I would be very thankful if someone give me hint or advise.

Thanks for reading it.