He can only archery hunt. A black powder rifle is still considered a firearm for the purposes of the prohibition for convicted felons.

Here is the definition from the statute:

Connecticut General Statutes, Sec. 53a-3. Definitions. Except where different meanings are expressly specified, the following terms have the following meanings when used in this title:

(19) "Firearm" means any sawed-off shotgun, machine gun, rifle, shotgun, pistol, revolver or other weapon, whether loaded or unloaded from which a shot may be discharged;

Here is the statute that prohibits the possession:

Sec. 53a-217. Criminal possession of a firearm or electronic defense weapon: Class D felony. (a) A person is guilty of criminal possession of a firearm or electronic defense weapon when such person possesses a firearm or electronic defense weapon and (1) has been convicted of a felony, (2) has been convicted as delinquent for the commission of a serious juvenile offense, as defined in section 46b-120, (3) knows that such person is subject to (A) a restraining or protective order of a court of this state that has been issued against such person, after notice and an opportunity to be heard has been provided to such person, in a case involving the use, attempted use or threatened use of physical force against another person, or (B) a foreign order of protection, as defined in section 46b-15a, that has been issued against such person in a case involving the use, attempted use or threatened use of physical force against another person, (4) knows that such person is subject to a firearms seizure order issued pursuant to subsection (d) of section 29-38c after notice and an opportunity to be heard has been provided to such person, or (5) is prohibited from shipping, transporting, possessing or receiving a firearm pursuant to 18 USC 922(g)(4). For the purposes of this section, "convicted" means having a judgment of conviction entered by a court of competent jurisdiction.

(b) Criminal possession of a firearm or electronic defense weapon is a class D felony, for which two years of the sentence imposed may not be suspended or reduced by the court.