French drain needed

Hello, We need to install a french drain/soak-away in our small BK backyard. We’ve been experiencing a pooling of water when we’ve had heavy rains. Our drain can’t handle heavy water flow from the roof and general rain. Multiple plumbers have checked our drain noting there aren’t any clogs. I have also called the city because we believe the backup may caused by the city drain our pipe runs into. Any reccos for expereinced contractors who could doing this kind of work? Thanks!!