That is my view, be aware but don't necessarily be alarmed at this time. Anyway here are just a few suggestions hopefully to help the OP.
9 hour time difference between LA and Paris, jet lag is unavoidable. Just try to stay up as long as you can the first day.
2 hours a day extra daylight compared to LA, it should be light till around 10pm in Paris and later in London. It allows for a lot of evening sightseeing.
June is a great time to visit, second only to September in my opinion, but Northern Europe is wet, be ready for rain. The difference is that the rain is usually light compared to rain in the US so people just go about their business more or less as usual. Have a good lightweight rain jacket and a small umbrella, you can go anywhere and do anything.
I highly recommend the Eyewitness Travel Top Ten guide books. They are light, easy to carry in your pocket, cheap and filled with useful information.