Accélérer - to accelerate
Allonger le pas - to walk faster, to quicken one's pace
Arpenter - to pace up and down
Atterrir - to land (plane, bird)
Avancer - to advance, to move forward
Bondir - to leap, to bound, to jump forward
Caboter - to sail along the coast
Caracoler - to prance, to move proudly (horse/person)
Cavaler - to dash about/to run around
Chanceler - to stagger, to totter
Cheminer - to walk or proceed steadily (often path)
Clopiner - to hobble, to limp along
Courir à toutes jambes - to run as fast as one can
Crapahuter - to trek, to march over rough terrain (slang, military)
Crocheter une porte - to pick a door
Déambuler - to stroll, to amble about
Débouler - to come tumbling/rushing down/out
Décoller - to take off (plane)
Déferler - to sweep/roll forward (wave, crowd)
Dégringoler - to tumble or fall down rapidly
Déguerpir - to clear off, to scamper away
Dévaler - to run/rush down (a slope, stairs)
Distancer - to outdistance, to pull ahead of
Embrayer - to clutch (car), to start moving (fig)
Enjamber - to step over, to stride across
Escalader - to climb (a wall, mountain)
Faire du jogging - to jog
Faire du lèche-vitrines - to do window shopping
Faire du surplace - to tread water (swim), go nowhere (bike, traffic)
Faire le trottoir - to walk the streets (soliciting)
Faire les cent pas - to pace up and down anxiously
Faire marche arrière - to back up, walk backwards
Faire une ascension (de) - to climb a mountain/hill
Filer - to speed off, to dash
Flâner - to take a leisurely stroll
Fouler (le sol) - to set foot on, to tread
Fourmiller - to swarm with movement
Franchir - to cross, to clear (an obstacle)
Galoper - to gallop (horse)
Glisser - to slide, to slip
Gravir - to climb, to ascend (slope, mountain)
Grimper - to climb (tree, ladder)
Hâter le pas - to quicken one's pace
Marcher à quatre pattes - to crawl on all fours
Marcher au pas - to march in step (military)
Nager en eaux troubles - to fish in troubled waters
Nager entre deux eaux - to sit on the fence
Pagayer - to paddle (a canoe
Patauger - to splash about
Piétiner - to trample, to stomp
Plonger - to dive (water)
Presser le pas - to hurry, to quicken one's pace
Ramper - to crawl/to creep
Randonner (faire une randonnée) - to go hiking/trekking
Raser les murs - to hug the walls (shyly, furtively)
Rattraper - to catch again, catch up
Récupérer - to retrieve, pick up again
Rouler - to drive/travel by vehicle
Ruer - to kick (horse, donkey)
S'accrocher à - to hang onto
Se balader (à/dans) - to take a leisurely walk
S'ébattre - to frolic/romp about joyfully
Se cabrer - to rear up (horse)
S'échapper de - to escape from (place)
S'égailler - to scatter, disperse
S'élancer - to dash forward
Sauter - to jump, to leap
Sautiller - to hop, to skip
Se faufiler - to slip through, sneak through a crowd/gap
Sillonner - to travel over (area) extensively
Stagner - to stagnate, to be still (water)
Tanguer - to pitch (boat, aircraft)
Tituber - to stagger, to totter (drunk)
Traîner - to linger, to hang around
Traîner les pieds - to drag one's feet (literally+fig)
Tramper - to trudge (Swiss)
Trébucher - to stumble, to trip over
Tressauter - to jump, to give a start (from surprise)
Trotter - to trot (horse); to run/bustle about
Trottiner - to bustle about; to walk with short, quick steps
Valdinguer - to take a tumble (slang)
Virevolter - to twirl, to pirouette
Virer - to turn/to swerve
N.B. - French focuses on destination rather than method; "I walk to school" turns into "I go to school" and requires a gerund if you want to specify the speed or vehicle (+ en voiture, en courant, etc).