I would like to travel to Paris in the middle of August with a group of friends. Is this a bad time to visit Paris if many part of Europe shut down for the month of August? Would I be limited as to what is available such as museums, churches or basic services like resturants, local sites or boats on the Seine?
This isn't a bad time to travel to Paris - you'll likely see a lot more tourists than Parisians though as most of them go on their vacations during August. However, Europe doesn't shut down - all business that you'll need are open (they'd miss out on all the tourist money!) You won't have any problem finding a place to eat and all the tourist sites stay open. Boats run as scheduled and there will still be lots of shopping and markets open! Plus, the weather should be fairly warm and dry and you'll have lots of daylight!
I went to Paris in August and it was just fine. Only a very few restaurants were closed, but all of the sites, churches, museums, boat tours, etc. were all open. You won't be limited at all.
This posting is probably too late since it's already middle of August. But, we travelling in August in Paris many times and didn't run into issues with the site and restaurants. However, lots of shops will be closed for the month siting their "vacances annuelle", but with sooo many shops in Paris, you won't be at a loss at all. As already said, there will be lots of tourists there -- as long as it's something you're expecting, you won't think anything of it.