Will taxis in Paris take charge cards, or must I pay in euros?
Theoretically they do, but always check before you get in as some of them have 'broken machines' or otherwise don't take cards. It is always wise to have enough local money to be able to make a small purchase like this.
We only took a taxi once and we paid in Euros.
In addition to taxis, consider taking the Metro. Once we were oriented, the Metro took us everywhere we needed to go. On Saturday morning, we rode the Metro to Cemetery Pere Lachaise. We were serenaded by an accordion player playing typical French accordion music. During rush hour the Metro was crowded, but we had no problems. We had our money tucked away safely and practiced situational awareness.
Any estimate of how much it would cost to take a taxi from the Marais area (Hotel de ville) to Trocadero? Are there taxi lines in the area (or use an app or something)? We have a tour leaving at 0630 and plan to take the Metro. Just a little nervous about having enough time that early in the a.m. Then again there's no guarantee a taxi will be available or show up at 0530 or so.
There's an important thing to notice with Paris taxis, how to tell the difference between official city taxis and cab companies that will charge you more. It's easier to spot in New York (yellow is the way to go, but look for the medallion with the 8X88 combination of numbers and letters on the hood, which matches the license plate) or London (licensed taxi drivers in their Hackney carriages have their distinctive vehicles, rail station taxi ranks will only allow official London cabbies there (and the cabbies police this very effectively... I've seen fly-boy private cab company drivers try to join the queue and the official drivers will confront them and call the British Transport Police office at the station within five seconds!) but not so much in Paris (where private cab companies can line up right outside the Gare Du Nord and charge 40 Euros for a trip that should cost less than 15 Euros if you walk to the official taxi area with its metal railing on the west side of the station).
But once you know the little things to look for, it's dead easy to spot a licensed cabbie. So here is your "how to spot an official Paris taxi" guide.
Official Paris taxis have white TAXI PARISIEN on a sign the roof, with colored lights under the sign. If the sign isn't white, or it just says TAXI, and it doesn't have the "fare zone" lights on it (frequently those little lights have letters on them... might be three, might be four), it's not an official city cab from one of the official companies.
The white roof sign is sometimes illuminated with green LEDs when the cab is vacant, and with red-amber LEDs if the cab is occupied or on its way to pick up a customer. If a taxi waiting at the station don't have the green LED lights behind their white facade at night, it's probably not an official Paris taxi.
Taxis can come in all sorts of colors and advertising or sponsorship, but only the official ones will have a metal plate on the outside of the vehicle (front right wing, either up near the mirror or lower down near the wheel arch) showing the taxi license number. Only official taxis will have this on the front passenger side (and if you're from Hong Kong / Britain / Australia, etc., remember that the passenger side is what you'd first think is the driver's side). Look on the front right wing.
Metro trains start at 0530 so you should have enough time. For Hotel de Ville to Trocadero take Line 1 to Franklin D Roosevelt, and Line 9 to Trocadero.