How can I get rid of gnarly roots in an outdoor French drain without hiring/renting a roto rooter
Is the pipe completely clogged (water doesn't flow)? If so, I would attempt to find a solution quick, especially if the temperatures where you are at are below freezing. Standing water would not be your friend in the near future, and you may end up having to replacing some drainage pipe.

I am going to have to agree with Carl Witthoft on this one. I'm not sure a home-made solution would be of best practice here unless you have a manufacturing shop and an engineering degree. I would suggest renting a drain auger from a home improvement store, or local rental supply company, and feed that down the pipe. That thing will make quick work of any loose roots and get water flowing.

In the warmer months, I would look at root killer. There are some that you can poor down the drain and it will coat the pipe in a film that will prevent some of the nasty roots growing in the pipe.