Whenever I need to go to the hectic area around the Opéra Garnier, I make sure to go for an early after-shopping dinner in the rue Sainte Anne, hidden just behind all the large boulevards. The rue Sainte Anne is the heart of the Japanese district of Paris, or actually rather a district by itself.
I cannot think of a restaurant or shop in this street that does not in any way relate to Japan. Even the boulangerie mixes green tea into its pastries. Some Korean restaurants break the Japanese hegemony, but they remain a minority.
If you’re up for ramen or other Japanese hot dishes, the choice is large. I find many of the restaurants quite similar and usually judge them by the queues (and then try to go there earlier a next time!). For hot summer weather I particularly recommend two places:
Firstly Aki Café (75 rue Sainte Anne) is a lunch room that sells fresh salads with udon noodles and sea weed, gorgeous pastry and several dishes of the day for reasonable prices. Do come here for an early lunch, before all the office people drop in.
Second: off rue Sainte Anne, a few streets further on rue d’Argentueil you will find people queuing at Sanukiya. They make their noodles right before your eyes and their other ingredients are just as fresh. Their cold noodle dish is in my eyes the ideal summer delight!