Uber

I don't take them on principal, anywhere, but they currently are under fire in a number places in Europe including Paris for their practices.

If you travel soon they may be OK, there is a chance that if you travel months out that there may have been changes.

My daughter used Uber from Rue Cler to the airport and another friend used Uber a great deal in Paris about a year ago. Both had very good experiences.

Thanks, Alison. We have to get to our apartment in Rue Clare from Gare du Nord by a specified time and I'm worried it may take a while to get a cab.

Taxis aren't a problem; you just get in the taxi line, which may look long, but it moves up fast. I'd opt for a licensed cab driver with known auto insurance. That has been an issue in France, as it has been here.

Most people are unaware but French cab drivers have to pass stringent exams, know which roads are blocked by deliveries, emergencies, etc. at what time of day in order to avoid them. Additionally, they pay high fees before they can get behind a wheel. This wasn't the crux of your question, but I'll add anyway that people are always watching out not to be cheated, and drivers are aware of this and try to ensure confidence. They are really quite honest in Paris.
ONTOH, where I live, Uber could be just as good as these untrained drivers we have around here.

Adding to the point Bets is making, we had excellent service from TaxisG7 in Paris. They are the largest there, and get rave reviews. There is an English speaker line to call. While I like some aspects of the Uber concept, I see no reason to complicate it when there is very good taxi service, and plenty of it, available. That's just me, though.
Have a great trip.

Thanks, all. Taxi it is!