This is an interesting picture. Where did you find it? The Chasseurs did not normally wear greatcoats on campaign, and the headgear is unusual as well. The chasseurs are usually represented wearing the kepi in 1859, but this man seems to be wearing a squat version of the full dress shako, but with an oilskin cover.
Anne S K Brown collection
The french Foreign Legion at Magenta wore Heavy greatcoats in boiling weather if I am to believe the re-enactors i saw last year. See the blog and the post TOO HOT AT MAGENTA