The tourist season starts in late June in the Alps. Early July is not too crowded, but the tourist density increases as the month progresses, and once schools have closed for the summer, and particularly as many Europeans have vacations in August., the density reaches a peak in August. The seasons have evened out a bit, as traffic density from many Asian countries has increased in recent years, and is not synchronized with the European patterns. September is calmer, except for the marathon weekend, and the weather - on average - is better.
The north shore is as described, and is an excellent idea, if you drive, with one minor exception. Specifically, Last year I chose to stay in Thun on the Saturday of the Jungfrau marathon, September 8th, and then drove to Interlaken and Lauterbrunnen along the north shore on Sunday about midday. The road was "ein Stau" - a traffic jam - of slow moving northbound cars from about half way between Merligen and Günten. Southbound was easy. Of course, I could not really look at the scenery unless I stopped and pulled off the road, because I was driving.
I assume that you will not be let lagged, since you will be coming from Paris.
Your itinerary as described fits well to train travel. The one place where a car is notably faster - one hour roughly as opposed to just under 2 hours by train - is the scenic journey from Interlaken Ost to Luzern. You have selected the train for that journey anyway. Also, if you have a group of people, rail passes or rail travel for all of them can be more expensive than renting a car. But, the car is an expensive pain in the neck if you visit cities, and is of no use in car-free areas, such as much of the Jungfrau region. I have a travel pattern which disregards cost and maximizes convenience. After a couple of jet lag days in Zürich , visiting friends and eaing well, if expensively, I rent a car, use it to get to various villages where I stay, and use the train to go into all the cities and for most other journeys. Public transport to trail heads has diminished over the years, as more people use cars, so I find one useful for that , and for getting to out of the way places for photography. The attached panorama was taken on a hillside above Sumiswald in the Emmental, and a car was the only convenient way to get up there and check out several viewpoints over a period of a few days. I walke up above Trubschachen for the image of Trub. I do use a car to go into Luzern, sometimes, because it is not hard to go to the main station and leave the car there. Unless your hotel has some special parking arrangements ( my choice does not) you'll end up spending on the order of 50 -60 USD to park overnight. Hardly an inexpensive process.
You are wise to stay several days in the Jungfrau region. The weather my not be cooperative on any given day, and if you go up to Jungfraujoch when it is in the clouds, you get a very expensive view of the inside of clouds.
I like to stay in Wengen, actually in the Alps, because Interlaken has no charm (in my opinion) but with your travel plans, Interlaken is a good base. Day 4 might work better if you stay in Grindelwald, which is my least favorite town in the area. More commercial and more spread out than the other alpine villages.
<<"Any other places I can visit in this area?">>
Just a few. You'd probably run out of them in 3 or 4 weeks. ;-)
Lots to do in the area:
This link discusses the "where to stay" options:
Here a few more details:
I really like this walk, in the direction towrd Kleine Scheidegg, becaus of the way that the Eiger grows over you as you walk the trail:
You have filled your days. I'd spend serious time with the timetable to work out the travel times. You may have trouble fitting in all the things that you list and doing justice to them..
Please make sure to read all of the tips and tricks on this page before diving into the timetable for the first time:
Your day #4 might not give you a lot of time to actually do much but look around rather quickly.