That's a very French things to do. Over here, people just sit in parks or cafes by themselves for hours gazing at the scenery and passerby. I personally love biking near the river and just sitting and watching it. Yesterday, I was walking back from the grocery and just stopped and sat in this memorial area near a fountain for 10 minutes. It's very refreshing.

You already know my opinions about cell phones and email...very useful but they get in the way of real life.