Babicka began his senior career in his native Gabon with Mangasport.[2]
Kiyovu
From 2018 to 2021, he played in Rwanda with Kiyovu.[3]
Aris Limassol
On 5 August 2021, Babicka transferred to the Cypriot club Aris Limassol, together with his compatriot Alex Moucketou-Moussounda.[4] He scored four goals and made six assists in the 2021–22 season in Cyprus, and was nominated as one of the best attacking players of the season.[5]
Toulouse
On 14 January 2024, Aris Limassol announced Babicka's transfer to French club Toulouse for a fee of €2.75 million, which was the record high fee received by Aris.[6]