If you cannot live without the internet, it makes sense to think through how you are going to get online in advance. Also, if you plan to purchase any activities online, it is best to do so before the trip.
Easiest way to get online
Most museums and parks in Paris have free wi-fi access. The connection speed is good enough to check your email or make a Skype call. Internet is also available at places like McDonald's or Starbucks (you'd need to buy something).
Internet in Paris hotels
While the situation is improving, most of Paris hotels offer rather slow internet connection service, if it is available. When you book hotel online before the trip, please pay attention to the customer reviews about the speed of internet connection. It is best to choose those hotels that offer not only wi-fi in the lobby, but have free in-room internet as well. Use Booking.com to book your hotel in Paris and see what other travelers are saying.
Pre-paid data card
If you need a data package in Paris, there are multiple options, but explaining what you need may get tricky. Similar to the phone prepaid plans, ask the sales assistant at the retail store that you need a prepaid data plan without a contract, La carte prépayée pour internet, sans engagement.
Because there are so many data plan options, after you purchase one, make sure there is in fact no monthly charge as canceling the data plan after you get back home will be a challenge.