Some of the first things I thought for "art inspired by primitivism" were the logos/posters for the Olympics and World Cup. They usually have a simple human figure formed from contour lines that we often see in cave art. These posters from the 1930 Uruguay World Cup and 2000 Sydney Olympics stood out as following those guidelines.
These posters from the Art Nouveau period reminded me of the illuminated manuscripts (The one on the left particularly remind me of the Book of Kells). They're both very decorative, have a detailed patterns, and flowing lines. Even though the text from the first poster is one of the simpler ones from the period, it' still has a decorative feel to it that matches the image.