Just a question, did you reserve the place already in Paris? Since you are talking about next week, not sure you can get into Septime. Give them a call to see if they can squeeze you in.
You should try their croissant Ispahan and pain au chocolat for breakfast. Just to make sure, Pierre Hermé doesn’t has a tearoom. You can buy his pastries and go to eat in a nearby café (we tried once), it wasn’t a common practice in France, but since it is Pierre Hermé, the cafés are used to it. There is Bar Chocolat Pierre Hermé au Royal Monceau, but it is only for the afternoon tea.
Stohrer - I tried several times, they never really impressed me. If you like pastries, you can try the salon de thé of Jacque Genin, he makes the best lemon tarts in town. But recent years he tried to make chocolates and he still continue to make limited pastries for his tearoom. 2 shops in Paris.
For your information, Ladurée has changed chef, Claire Heitzler is now heading. They have shops and tea salons across the city. I also like a lot Christophe Michalak. You can read more about sweets on this thread.