Building a rain garden from existing french drain

I have an existing french drain that goes from one corner of the front of my house across my lawn diagonally. It ends right before the street. When I moved in, I could tell the previous owners had the sump pump routed to it, but that had been disconnected and run into the sewer line, so it wasn't in use. I have since put in a rain barrel and directed the overflow into the pipe of the french drain.
I'd like to simply dig a rain garden somewhere in the lawn on top of the french drain, and cut it so it flows into the rain garden. I guess the other end of the pipe could be bent up and sort of used as a spillway? Does this make sense to do? I figured since the pipe is already buried and coming from my downspout, it's one less thing to do.
Any advice or ideas would be appreciated. I'm relatively new to permaculture but slowly trying to apply the principles to my suburban yard.

hau Nathan,

French drains are meant to move water down into the pipe and carry excess water away from a foundation, this is their usual reason for being installed.
Your description is not typical French drain routing, can you give more description of how it was constructed? Does it sit in a gravel bed? Is the pipe perf. pipe or is it solid pipe?