The cartoon features a man walking on an infinite line. The man himself is drawn using one line and is a part of the line he is walking on. The character encounters obstacles and often turns to the cartoonist to draw him a solution. The background color changes as mood or feelings of the character change, but most of the series was black and white. The cartoon was originally used for advertisements, before the animated series was created.
TV5 has 35 episodes to watch on-line, just choose one by the name. Another option is watch some of them at Daily Motion. The episodes available are 01, 02, 03, 05, 06, 08, 101, 105, 107, 110, 112, 114, 116, 125, 126, 127, 132, 133, 138, 149, 154. Don’t miss a funny episode (and I’m not sure if that is an original) with the title La Sexilinea and this funny parody. (via wmmna)
Update: TV5 updated the page with La Line videos, and now there are 56 animations to watch there! Cool.