Personally, I would have just kept my original rental agreement intact, but if changing from one arrondissement to another makes you sleep easier, so be it - this is your family, your vacation and your money. But the Ile St. Louis does not have some invisible dome surrounding it that magically ensures complete safety from terrorists. The message they wanted to send was that they can enter the most seemingly benign places - a restaurant, concert venue or sporting event - and carry out a seriously heinous act. They are not going to be limiting their opportunities to just 1 or 2 neighborhoods which is why, IMO, I would have just kept my existing reservation intact.
As for the apartment owner who just got your cancellation getting annoyed and keeping your deposit, let it go. You said it would be difficult for you to find another place on such short notice, so put yourself in his shoes - he was expecting to earn some income from your stay and you just cancelled on him. Now he has to find someone else willing to rent, but that may not be particularly easy given the short time-frame and the fact that this event just happened and many other cancellations are occurring all over the city for similar reasons. If he is able to get another rental and you get some more of your money back, that would be great, but if 100s of others are applying the same mindset as you and dropping their reservations, then you are correct to assume you will likely not see any more money back from the broken agreement.
On another note, a previous poster mentioned "Newton"; however, Sandy Hook occurred in Newtown, not Newton - not that the average tourist would ever have reason to really visit either Newtown or Newton… However, here in Boston, we had our own terrorist strike at a very well-known event and the subsequent police chase effectively shut down the city. I would really hope that you don't consider Boston off-limits to your children as they get older and start to learn more about the history of the U.S. Just like Paris, New York, London, Washington and Madrid, we don't want our cities to be avoided by travelers because of these tragedies.