The Place Saint-Michel [where the Café Musain was located] was situated at the intersection of the rue de la Harpe, the rue Saint-Hyacinthe, and the rue d'Enfer at the location where the Place Edmond-Rostand is today. The breaking up of the boulevard Saint-Michel transformed this part of Paris: the rue Saint-Hyacinthe is our rue Malebranche. The square that we now call the Place Saint-Michel and which is the entrance to the boulevard, near the Seine, was then called the Place du Pont-Saint-Michel.
The rue des Grès is the modern-day rue Cujas.
-The café Lemblin was at Palais-Royal, 100 and 101 galerie de Chartres. It owed its success to the excellence of the hot chocolate, tea, and coffee that were served there. It became a meeting place in the evenings for Bonapartist officers.
-The café Voltaire was, and still is, at 1 place de l'Odéon.
-Mère Saguet's cabaret, in Plaisance, was frequented by writers and artists, including Victor Hugo. The honor of discovering the restaurant, however, went to Hugo's brother Abel, who was nicknamed the "Christopher Columbus of Mère Saguet's."
The boulevard du Maine is now known as the avenue du Maine.
The barrière de la Cunette was at the extremity of the quay d'Orsay, at the junction of the quay d'Orsay and the boulevard de Grenelle. The barrière du Combat was at the end of the rue Grange-aux-Belles, in the location of the present-day place du Combat.
The Rue Plumet, originally Blomet, is now known as the rue Oudinot. There currently exist both a rue Plumet and a rue Blomet in Paris, but they're more recently named and aren't the original street.
The rue Mondétour ran between the rue du Cygne and the rue des Prêcheurs. The rue des Prêcheurs currently exists between the rue de la Cossonnerie and the Rue Rambuteau, into which the rue de la Chanvrerie has disappeared. Today the rue Mondétour runs between the rue Rambuteau and the rue Turbigo.
The rue Rambuteau was built in 1838 and absorbed the rue des Ménétriers (between the rues Beaubourg and Saint-Martin), the rue de la Chanverrerie or Chanvrerie (between the rues Saint-Denis and Mondétour), and the rue Traînée (between the rues Montmartre and du Jour). (From here.)
Please note that all instances of "now" and "currently" refer to the time of this edition's publication, 1951. Though I have checked most of these streets in the Nomenclature des voies database (usually available by typing a Paris street's name into Google) and confirmed that they still exist as named here, further changes could have taken place.