On top of all the valid reasons that have already been mentioned, it's important to understand that this level of micromanagement is not the way the French government (at least) is approaching things so far. The government has defined things like information or food as basic needs and allows all businesses in this category to keep operating. For example, there has been no decision to open supermarkets while closing bakeries, cheese shops or fish mongers. And there are anecdotal reports of people making a trip to the pharmacy and buying some cosmetics products just to keep busy.
Furthermore, note that many commentators are criticizing these measures for being too lax, giving too much weight to economic consequences over health concerns and relying too much on calls to the public to limit movements rather than harsh coercive measures. In France, the list of businesses that are currently allowed to stay open include auto parts shops, computer and phone shops, temp agencies, banks and insurance agents, laundry services and of course everything that is not open to the public including construction, manufacturing and deliveries of all kind. There are calls to pause all that but at this point, economic activity is not restricted to absolute necessities.
Conversely, as late as Thursday or Friday, bookstore owners were complaining about lasting damage because online retailers could still operate and were asking for an exception to the restrictions (as is the case in Belgium). I would be surprised if this happens but the minister of the Economy and Finance would not immediately rule it out.
Incidentally, online or even TV news is in a large part based on newspapers stories that are copied and commented all over the place. It might eventually come to that but it's difficult to tell newspapers “you're going to continue to offer contents for free but we will just deprive you on one of your revenue streams and favor your competitors in other media”. Here again, it's legally and politically easier to make the decision at a more general level and at this point, information is deemed important enough. Along the same line, many tobacconists also sell newspapers. It's extremely difficult to imagine closing these shops.
Finally, while the national rules are couched in very general terms, local authorities are allowed to take additional measures. For example, municipalities have closed parks or specific landmarks and at least one mayor specifically banned going out to buy just one baguette or newspaper (you are supposed to make more substantial purchases and stay at home in between).