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This soldier wearing a metal cuirass with a high helmet indeed belongs to a "cuirassier" regiment. You will find detailed information at Line Regiment nΒ°18.
His long beard looks rather unusual for the time (it was fashionable during the 2nd Empire to wear the same mustache and goatee beard as Emperor Napoleon III). A very likely explanation is that he belongs to the "sapeurs" (English: sapper) branch, who build fortifications, repair or build bridges, roads, etc. during military campaigns. It was a tradition for them, still preserved in the Légion Etrangère, to wear this kind of beard ; such a bearded soldier can be seen on the first painting of the indicated site (with specific axes on the sleeve); the legend of the painting mentions that this "cuirassier-sapeur" was part of the Imperial Guard, explaining maybe why this photo was taken in Paris and not in some remote garrison town.
His right hand glove is held in his hand. Is it a testimony of good manners ("etiquette"), as if he was ready to shake the hand to somebody ?