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Post Malone seems to be moving on after a couple breakups in quick succession ... looking very flirty with a mystery woman while walking through Paris on Thursday.

The two were spotted strolling around Rue Saint-Honoré and the Place Vendôme ... two iconic locales in The City of Lights. Backgrid

Posty's wearing a cowboy hat and a brown leather jacket ... while his gal pal seems a bit more attuned to the Parisian style -- wearing a dark overcoat and tall boots. Backgrid

While the two walking around together wouldn't necessarily signal anything romantic, they were also seen seemingly holding hands ... she even looped her arm through Posty's -- a gesture that certainly raises questions.

We know he's been officially single recently ... back i

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