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Romeo Beckham 's looking to mend his broken heart in the City of Love ... painting Paris red after his shocking split from girlfriend Kim Turnbull .

The son of David and Victoria Beckham walked the city streets Friday night in a toned-down ensemble ... sweats and a beanie on. Getty

He's not crying over his lost love in these pics ... but, he ain't grinning either -- instead staring straight ahead with a stony expression and occasionally checking his phone.

We don't know what he's looking at on his phone, but we'd guess it's not a text from Turnbull ... 'cause we confirmed the two are dunzo after their relationship caused quite the Beckham family spat. Reports confirm the breakup was amicable. Play video content

As you know ... Romeo's brother Brooklyn Be

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