Fenyvesi joined Fidesz and Christian Democratic People's Party (KDNP) in 1997 and 2006, respectively.[3] He was a member of the local representative body of his birthplace Ajka from 1998 to 2014. He served as a member and vice-president of Veszprém County Assembly between 2014 and 2018.[3] Fenyvesi was candidate for Fidesz in the April 2015 by-election in Tapolca constituency, which was held following the death of MP Jenő Lasztovicza. Fenyvesi was narrowly defeated by Jobbik candidate Lajos Rig, which was the ruling party's second surprising defeat in that year.[5]
Fenyvesi was again nominated his party's candidate in Tapolca during the 2018 Hungarian parliamentary election; this time he defeated Lajos Rig by margin of victory of 6 percent. In the parliament, Fenyvesi was involved in the Committee on European Affairs and the National Cohesion Committee from May 2018 to May 2022. He was also vice-chairman of the latter committee since October 2018. In addition, he was a member of the Subcommittee on the Implementation, Social and Economic Impact of Laws and Deregulation Processes of the National Cohesion Committee.[4] For the 2022 Hungarian parliamentary election, Fenyvesi was replaced by Tibor Navracsics as candidate of Fidesz in Tapolca (Veszprém County 3rd constituency). Fenyvesi admitted "Navracsics has a better chance of defeating of joint opposition candidate Lajos Rig". Navracsics ultimately won the mandate.[6]
