No, this list does not contain soup kitchens or homeless shelters. It's up to you to find those locations from other sources.
In her February 4 post on Guide Alternatif, French writer Carole Blomme lists eight Paris restaurant-cafes that offer free food to customers who buy something to drink.
Granted, the food isn't fancy, generally either couscous or moules frites (steamed mussels with a side of fries), and the eats are free only during limited hours on certain days of the week. Not that one shouldn't ever look a gift horse in the mouth.
- La Cordonnerie, 142, rue Saint-Denis (métro Réaumur Sébastopol, line 4), offers free couscous every Thursday and Saturday after 8:30 pm.
- Le Tribal Café, 3, cour des Petites-Ecuries (métro Château d’eau, line 4), serves free moules frites on Wednesdays and Thursdays after 9:00 pm. On Fridays and Saturdays, couscous is free after 9:00 pm.
- La Chope du Château Rouge, 40, rue de Clignancourt (métro Château Rouge, line 4), serves free couscous on Friday and Saturday evenings after 9:00 pm. Beer is only 2 euros.
- Le Taïs, 129, boulevard de Ménilmontant (métro Ménilmontant, line 2), serves free food after 7 pm four nights a week: free moules frites on Wednesday and Thursday evenings and free couscous on Fridays and Saturdays. Beer is 2 or 3 euros.
- Le Grenier, 152, rue Oberkampf (métro Ménilmontant, line 2), serves free couscous on Saturdays after 7 pm. You may also be able to catch a jazz or pop concert there on the weekend.
- Les Trois Frères, 14, rue Léon (métro Château Rouge, line 4), serves free couscous on Thursday evenings and free soup on Sunday evenings, both nights after 9:30 pm.
- L’Eclipse café, 13, avenue de Saint Ouen (métro La Fourche, line 13). A slightly different twist: attend a concert for 3 euros and eat free couscous afterwards.
- Les Fontaines, 153, rue Saint-Maur (métro rue St-Maur, line 3) offers free couscous Friday and Saturday evenings.
Caveat: Sadly for my wallet, I did not know about any of these establishments during my recent stay in Paris, so I cannot vouch for their ambiance. If you have more information to offer, please feel free to comment.