In French, there are different ways to express the notion of "walking", depending on the context.
Marcher is used to describe the action of walking in general, or the way a person walks:
Aller à pied
Aller à pied (literally going by foot) is used when walking is contrasted with another means of transport - walking instead of driving for example - and is always followed by the destination you're getting to:
Se promener means to take a walk / to walk, wander around.
It's literally "to walk oneself" :
You can also use faire une promenade or se balader :
Promener means to walk [someone/something] (i.e. a pet...):