For single-place powered paragliders, the answer is simple, they do not fall under Sport Pilot. If it weighs less than 254 pounds, it’s an ultralight and falls under part FAR 103. Even with wheels, it just has to meet the requirements of weight, speed and fuel capacity.
For two-place foot-launched operations the answer is also simple, they are not part of Sport Pilot and can only be flown under the exemption held by USPPA for appropriately qualified pilots (or ASC for $100/yr).
Two-place wheel-launched operations are Powered Parachutes. The craft must be certified (with an N-Number) and flown by a licensed Sport Pilot.
The FAA’s 14 CFR Federal Aviation Regulations part 1 definition:
A “Powered parachute means a powered aircraft comprised of a flexible or semi-rigid wing connected to a fuselage so that the wing is not in position for flight until the aircraft is in motion. The fuselage of a powered parachute contains the aircraft engine, a seat for each occupant and is attached to the aircraft’s landing gear.”
A powered paraglider is not defined because it is not covered. But The original sport pilot issuance on July 27, 2004 further explained:
“As stated in the proposed rule, the FAA specifically intended to exclude from consideration as light sport aircraft configurations in which the engine and/or wing is mounted on the person operating the aircraft, rather than a fuselage.”