How can I make my legion faster to reach enemies quicker?

There are a few ways to do this.

Raiders have a marching speed bonus.

Research in each of the Legion research trees to reach and complete the alloy horseshoe item to increase the base speed.

This will also unlock the research commanding banner on the way which allows you to use speed up items to increase matching speed for certain marches. You need to win or buy these though with gems or alliance points.

Use only cavalry in the formation. These troops travel faster and if they are the only ones in the legion then you will march faster.