Any recommendations/tips/must do things while taking a short trip to Paris?

I'm sure we may spend more time here then originally planned due to the riots and not sure if we'll be doing London 

I hope the riots are done by the time you visit -- and that you have a fantastic time! Maybe you two should consider going to Bath or Salisbury!

Or even better - pop on over to Brussels and/or Amsterdam, an easy train ride away.

Wow, looks like I've gotta get myself to Paris! All this sounds amazing (and romantic!)

I'm sure we may spend more time here then originally planned due to the riots and not sure if we'll be doing London 

I wouldn't let the recent riots put you off - they've died down at the moment, anyway. They mainly occurred in places that tourists would rarely go. And there are so many police officers in London I think they're prepared to put down anything that starts again as quickly as possible. I would never say spend less time in Paris (I love Paris), but don't cut out London from your plans if you really want to go.

Just a word of warning regarding Montmartre/Sacre Coeur (this is true anywhere in Paris but these people are particularly present/aggressive at Sacre Coeur):

There are a lot of guys who hang around on the hill on the way up to the cathedral with embroidered bracelets, or sometimes snap bracelets. They will come up to you, put it around your wrist and then refuse to let go of your hand until you give them money. Don't feel obligated to be polite to them if they approach you - walk briskly past them, or yell at them if need be, but don't let them get close to you. (Sacre-Coeur is lovely though!)

Also, some fun things to do:

Walk from the Jardin de Luxembourg down rue Mouffetard (a historic, narrow, roman-era street) and get crepes from Le Petit Grec. Paris is famous for crepes but the French take-away crepe usually just make savory crepes with a combination of ham, eggs and cheese that are sort of floppy. This greek one makes it with lettuce, tomato and onion for no extra charge no matter what kind you order.

The woods on either side of Paris (Bois de Vincennes to the east and Bois de Boulogne to the west) are nice romantic places to take a walk. (Just stay away from Bois de Boulogne when it's starting to get late...that's when the prostitutes and their patrons start hanging out there.)

I always liked walking along the Seine at night time.