Transfer from St. Lazare to Gare Du Nord - timing, taxi?

No fixed rate, it goes by the meter. Worldtaximeter.com sys 8.25 EUR, so figure 8 to 10 EUR.

I would give myself 40 minutes. CityMapper estimates a taxi ride late on a Saturday afternoon (barring any protest marches anywhere near or anything else that further messes up traffic) at 20 minutes. If that is true, give yourself 10 (or 15) minutes to disembark from the train and find the taxi stand at Gare St Lazare, and then 10 (or 15) minutes to descend from the taxi and get oriented to where you need to go within Gare du Nord to check in for Eurostar.

Remember that you should be in line for Eurostar at least 60 minutes prior to your train's departure (or more, if they have lengthened the wait time, which wouldn't surprise me with the issues these days. I used to give myself 90 minutes, but I haven't taken Eurostar since 1) the pandemic and 2) Brexit came into effect.).

I would allow maybe a little more for the cost of the taxi, but I hardly ever take taxis so I am not sure why I think this

Thank you both, very helpful, I apreciate it.

They have lengthened the recommended times for Eurostar: travellers are now advised to arrive at Gare du Nord 90-120 minutes early instead of 60 pre-brexit.
Adding in travel time from Saint Lazare and possible train delays, I would therefore plan to take a train from Caen that arrives in Paris at least 180 minutes before the Eurostar leaves from Gare du Nord.

Listen to Balso; since all of the immigration and emigration processes occur at Gare du Nord before you depart on the Eurostar, you want to get there as early as possible. And note that cross town taxis can get very bogged down in traffic -- it is always better to take the train when you can IMHO. I'd be inclined to take the RER E from Haussman/St Lazare to Magenta (the stations tied to St. Lazare and Nord.). RER stations have elevators and escalators. This requires an ordinary metro ticket which you can get from a machine for 2.10.

Taxi is not a fixed fare from St. Lazare to Nord -- Fixed fares apply only at airports. I have had bad experiences with very long trips cross town and avoid taxis when time is an issue for that reason. Taxi is probably fine if you prefer but factor in at least 40 minutes. Anyone at a train station in town offering a fixed fare except to the airport is trying to cheat you. There have been reports of taxi drivers using the airport fixed fare for trips within Paris --at many times the cost the trip should be on the meter. Always use the meter in town. (and while there is a small drop fee on the meter, there is no charge for luggage or extra people up to 4.