I'm fond of the charming, delightful little restaurant
Roger le Grenouille which happens to be situated not far from the Seine if memory serves me right.
I wrote a little trip report on it once
here, but you'd do better to go there yourself next you're roaming the streets of Paris.
As for something else to do, once your belly is full with la bonne cuisine française, check out the
Parisian catacombs – certainly not a secret judging by the length of the queue, but a most fascinating thing indeed.
Bon voyage, mon ami!