Yes, it's possible. A loop around city park from my house in this neighborhood comes out to be a little less than 10 miles.
Frenchman is more of a problem because of passing I10 and 610. If you went to City Park and then pick up Esplanade you can do it, but it's really out of the way. If you go down Elysian Fields you have a pretty long section that is all highway ramps, railroad and industrial stuff. Not only is it dangerous for bikes, the residents are some of the poorest in town and there are high overpasses without bike lanes. Not a fun ride.