- Put the origin of the curve at its beginning vertex (shift ctrl alt C > Origin to 3D Cursor).
- Disable the different Follow Path constraints of the character objects (you don’t need them).
- Switch your armature to Object mode, give it a Follow Path constraint, choose the curve as Target, enable the Follow Curve option.
- Clear the Location of the armature with an alt G.
- Rotate the armature the way it is supposed to be (R+Z+180).
- Select the curve.
- Open the Graph Editor, display the properties panel (N), open the Modifiers tab and deactivate the Generator (which is automatically created with the Follow Path but won't help you here).
- On the Timeline go to frame 0.
- Keep the curve selected and go to the Properties panel > Data > Path Animation, choose an Evaluation Time of 0 and and insert a keyframe.
- On the Timeline go to the frame you want, and in the Properties panel > Data > Path Animation, insert a new keyframe in the Evaluation Time with the value you want.
- In the Graph Editor, put your mouse over the graph and press T > Set Keyframe Interpolation, and choose Linear so that the movement along the curve is linear.
You can speed up the animation of the character along the curve with the Evaluation Time value.
You can speed up the walk cycle speed itself in the NLA Editor (right properties panel > Scale value).
But first, make sure first that no action is loaded in the Dopesheet editor, otherwise this action will play over the NLA strip.
Also, note that you can quickly edit the action of a NLA strip, selecting the strip and pressing Tab. The pin (on the left of the track) will allow you to see the animation with or without the NLA settings effect.