From their definition, the only difference between a rifle and a shotgun is that the first one has a spiraled barrel and the second a smoothbore, the two being shoulder weapons. The proper translation in French should then be:

• Rifle = carabine
• Shotgun = fusil (de chasse)

To be honest, I doubt 0.1% of the population would be able to tell the actual difference between carabine and fusil (I did not know and I will forget very soon, to be honest).

Also, in the military, shoulder weapons are usually called “fusil”: fusil d’assaut (assault rifle, generic term for war guns), fusil sniper (sniper gun), fusil (semi-)automatique (semi-automatic rifle/machine gun) (1)

Fusil is usually used in informal talks as carabine is often associated with “carabine à plomb” (pellet gun) nowadays. However, it is rather common to see the word carabine in news titles like “un homme tué par une carabine” (a man killed with a rifle/shotgun), but it can be either a rifle or a shotgun.

More on guns

You have not asked but I will answer anyway:

• Arme à feu = firearm
• Arme de poing (“fist weapon”) = handgun, i.e. firearms which are not shoulder weapons
• Chevrotine = buckshot

(1) For years, French military was equipped with semi-automatic rifles called FAMAS (Fusil d’Assaut de la Manufacture d’Armes de St-Etienne) which is being replaced with HK 416 F

If one takes the definition that a rifle is a gun with a rifled barrel, and a shotgun is a smoothbore barrel, then one could say

• Fusil à canon rayé

• Fusil à canon lisse

However, as you already observed, this difference is not commonly used to categorize weapons. Instead, looking at a sample of French gun retailers online, the purpose is often used (fusil de chasse, fusil d’assaut, carabine de tir longue distance, etc.), the reloading mechanism (fusil à pompe, fusil semi-automatique), or even just the ammunition stock (carabine 22 long rifle).