Watch the After Paris: Melody online guitar lesson by John Knowles, C.G.P. from Fingerstyle Journals
When I play "After Paris", I'm keeping a pretty steady, alternating thumb with an occasional reference to the intro rhythm. If I were using a thumb pick, I don't think I would mute the bass strings. Notice how the second phrase works like an answer to the first one. Then the melody continues with two short phrases. I'm using my right index and ring fingers when I'm skipping strings to harmonize the melody. The next phrase is a longer answer to the two short phrases. And now I'm back at the beginning phrase followed by a concluding phrase. At that point, I can go back to the intro or play the ending.