I was in Paris in June and was also surprised by the police presence. We were unable to get close the Eiffel tower that day because the area was closed off. Supposedly there was to be a motorcade coming through, but we were around there about an hour and nothing came. The police are everywhere, with full gear, vests and rifles.
But then, we went to a train station to take a train to the south of France, and we boarded the train with our luggage, and no one asked for our tickets or even looked our way the whole time. We just got on and rode for 4 hours. Go figure.