Right in the middle of the river just after the Pont des Arts, you'll see the pointed, protruding tip of the Ile de la Cité, the largest of the Parisian islands and the site of the city's oldest settlement. Here you can see a delightful little garden called the "Square du Vert-Galant", or the "square of the old gallant", as King Henry IV was nicknamed for having had many lovers, even when he was much older! The monument at the top of the stairs that descends into the garden depicts the king.
Immediately after passing under the Pont-Neuf, which despite its name meaning "New Bridge" is actually the oldest in Paris and from the early 1600s; Henry IV had it built to connect the palace of the Louvre with the abbey of Saint-Germain-des-Prés.
Immediately after Pont-Neuf, look to your left to see Place Dauphine, a pleasant clearing surrounded by libraries, art galleries, and small restaurants, where as readers of Simenon's novels know well, Commissioner Maigret goes to relax. Immediately afterwards, you can see the rising mass of the Palace of Justice.
After having passed under three bridges, one after the other, a very spectacular stretch approaches which includes an impressive view of Notre-Dame Cathedral. Don't miss this chance to admire the gardens, the cathedral's exterior, and especially its back with the beautiful Gothic arches.
After the archbishop's bridge, the boat turns around the back of the island, where you can see the Deportation Memorial dedicated to the martyrs of the Second World War. Then you'll pass under the Saint-Louis Bridge, which connects the Île de la Cité with the quiet island of Saint-Louis on your right, which shows 17th and 18th-century residential buildings in all their elegance.
Now that you're sailing in the same direction as the river's current, three large towers on the left will make it easier for you to find the 14th century Conciergerie palace, which was transformed into a jail and place of torture during the Reign of Terror four years after the Revolution. Above all of it, you can see the pointed spire of Sainte-Chapelle.
FUN FACT: when the "New Bridge" was inaugurated with a great ceremony, King Henry IV passed over it on a beautiful white stallion. The bridge soon became a landmark of Parisian life, and was always animated by vendors, jugglers, and dentists.