One way to become familiar with a culture and its language is to read its news. Paris Match is a weekly news, style and entertainment magazine from France. Le Figaro is a right-wing daily news publication; Libération leans left.
There is a Wikipedia list of newspapers in France, where you can find other sources (and some of them are available in English as well as French).
Here are a few websites that maintain lists of French resources. Many of the resources they list are free, but not all of them. Durham Tech provides the links below as a reference for interested students, not as an endorsement of the sites or their content.