There are two walking itineraries in the 'Paris Pilgrim' city guide. One is north of the Seine and takes about 2 - 3 hours. The other is south of the Seine (starting at the west end of Nortre-Dame) and also takes 2 - 3 hours. There are suggestions in the Guide for other places to visit in Paris as well.
In the middle ages Paris was the start of the long walk to St Jaques de Compostelle for hundreds of pilgrims from Germany, England, France as well as Sweden and Norway and the low countries.
Michener describes the clerics with their clerks and retinues, the Knights with their horses, their ladies and their servants, the devout laymen seeking salvation, the criminals, beggars, forgers, theives and robbers; merchants, architects, painters, masons and government agents. It seems there was never just one 'real' pilgrim! Much like today, I suppose!
The route from Paris was once the most used road to the various shrines in the south and to the Pyrenees and Spain. In 2004 (a Holy Year), when I walked the route, the pilgrim office registered 24 pilgrims who had started in Paris. Its still not a very popular route and in 2009 only 79 pilgrims started in Paris.