Is it better to buy the tickets e.g. Eiffel Tower online that buy it when we get to Paris?
If you buy in advance you run the risk of crappy weather - - and you might as well throw the ticket away and buy a new one on a better day.
Depends on when you're going and if it's important for you to be up in the Eiffel Tower on a specific day (ie for an anniversary, holiday, etc.) The lines for tickets (and to get the elevator up to the top) can be really long during peak times. Might be worth it to buy online then. Same goes for other attractions. If there's a convenience fee added to the ticket price, then I would say it's almost definitely not worth buying online.
We went last year at the beginning of October. When we arrived there was a huge line up to get tickets. Thinking we would wait til the next day, we began walking to the park. At the next leg of the tower the line up was only 5 minutes. Not sure if there was a group that was going up the other leg of the tower or what, but it might be worth just looking around to see if another line is shorter. I would just wait to buy the tickets unless of course you have a limited time frame and need to be there at a particular time.
For Eiffel Tower, I'd say yes buy ahead if you can. Lines in Aug were about 2 hours long. We bought online from our hotel 1 day ahead, so we had an idea that the weather would be okay. For Louvre, not really, arriving just after opening security line was about 10 min and buying entrance tickets from machine in Louvre was also about 10 minutes. But sounds like others have experienced longer lines. St. Chappelle - long lines. You have to wait in security line always but could buy a museum pass to bypass the ticket lines.
I went with my daughter at the end of July, and I was very glad I bought our tickets in advance. If not, line looked to be about 2 hours long around 8:00 p.m. Also, if you buy online in advance, you can specify the exact day and hour to visit. With an advance ticket, you're in probably in 15 minutes or so. You can't do anything about the weather anyway.
By the way, same goes for The Louvre if you plan on going there. Line was ridiculous. Glad I had my ticket in advance : )