Does a French drain need to terminate above ground?
Look at a typical "dry well" install - basically terminate the pipe into a blob of crushed rock, or an actual void/hole/tube punched full of holes, so the water can filter out. Just stopping the pipe underground will not work well.

In an essentially non-freezing climate there should be little problem with this - they can be done well in freezing climates, but it's more work and digging. If you use a open/void/hollow well it's easier to check/clear the pipe if that's ever needed.