Jean Dubois and Françoise Dubois-Charlier have made a global semantic classification of the verbs in French, the reference site for this database is at their homepage (in French). It features a browsable version of the database and many information documents.
I am not familiar with Levin’s classes, but this may be what you want. Regarding motion verbs, you may want to browse the generic classes “M: mouvement sur place”, “E: entrée, sortie”, “H: états physiques et comportements” and in certain cases “L: locatif”.
However, remember that this classification can’t be an exact equivalent, since English and French (motion) verbs follow two different paradigms¹, namely English is satellite-framed whereas (modern²) French is verb-framed. Basically, it means that “Running into X” is “Entrer dans X en courant” in French: in English the direction of movement is determined by the satellite (into) and the type of movement is determined by the verb ; it is the opposite in French. So any attempt to blindly apply a Levin-like classification to French verbs will fail.
² It is not true of Old French and there are still traces of it in Modern French, see the remarkable article of Anetta Kopecka The semantic structure of motion verbs in
French. Typological perspectives.