Born in Paysandú, López began his professional career at El Tanque Sisley. He made his debut in the Uruguayan Primera División on 14 February 2015, playing the final three minutes of a 1–0 home win over Montevideo Wanderers as a substitute for Facundo Barceló.[2] He played seven games over the season, all from the bench, and scored once on 7 June in a 4–2 win at Atenas in the last game of the campaign; the result kept his team in the top flight at the expense of the opponents.[3]
In January 2017, López transferred to fellow top-flight club Cerro.[5] On 14 May, his team won 3–2 at Peñarol to end that team's unbeaten season in the 14th game; he was sent off in added time after coming on as a late substitute.[6]
The next season he transferred to Progreso in the same league, contributing 14 goals to their promotion as runners-up in 2023. This included a hat-trick on 10 March in a 5–0 home win over Atenas in the second game of the season.[10]
Deportes Tolima
After scoring 10 goals in 17 games for Progreso, making him the second highest scorer by that point in the Uruguayan Primera División, López transferred to Deportes Tolima in the Colombian Categoría Primera A in June 2024.[11]
^Montaño, Pablo (15 January 2017). "Cerro: llegan Barboza y Franco López" [Cerro: Barboza and Franco López arrive] (in Spanish). Tenfield. Retrieved 2 June 2024.