A quick 40-minute train ride from the Gare de Lyon in central Paris takes you to one of the best day trips out of the city: a forest preserve surrounding a palace that dates back nine centuries.
The Forêt de Fontainebleau offers a hundred square miles of protected land for hiking, biking, and horseback-riding—all surrounding the magnificent Château de Fontainebleau. Although a castle has been here since the 1100s, most of the current construction dates from the Renaissance. Site of Napoléon I's abdication in 1814, this château is much less crowded than Versailles.
When I lived in Paris, this was the closest 'wilderness' available. If you want a break from the hectic urbanity of Paris, come to Fontainebleau mid-week; you'll feel as if you have a forest and château to yourself.