The plug on my headphones is bigger the headphone jack on the Fender G-DEC 3.
It sounds like your plug is a ¼” phono plug. The headphone jack on the Fender G-DEC 3 is 3.5mm. Luckily, most electronics retailers carry an adaptor to convert a ¼” plug to a 3.5mm plug. Once the adaptor is attached to your headphones, you will be able to connect them to the Fender G-DEC 3 with no problem.