instructions on how to get from Gare du Nord to Gare Montparnasse June 1

Fastest route would likely be the Metro line 4. There is a bus, but it would be almost twice as long. Otherwise taxi, which would cost more. Go to the RATP website to get more info. https://www.ratp.fr/en/itineraires

Do not take the bus, unless you are entirely unable to use stairs and cannot afford a taxi. It takes way too long and is too unpredictable. Average bus speed is now 6 mph in Paris...

Métro Line 4 is direct on paper, but there are stairs, and the metro station at Montparnasse is a solid 10-minute walk to the mainline platforms so you should build that in. You need to build that in.

A taxi is the easiest, straight-shot option . Sure the metro will get you there, but the stairs and carrying luggage would make me rethink it.

When are you traveling? It's might make a difference with availability of Line 4 or traffic. There is Bus 39. I would not plan on anything less than an hour by bus and it could be more than that. The metro should take around 35 minutes, including the long walk from the Montparnasse Bienvenue stop on Line 4 to the train station.

Good point: no line 4 on Sunday mornings for the foreseeable future, and some all-day closures every now and then.

Thank you very much. I will be arriving Gare du Nord at 1645 unfortunately - I'm trying to save money on the Eurostar ticket which I did not realize would be so pricey. Perhaps it would be better to just pay more and arrive earlier. I can deal with stairs and luggage so the Metro line 4 sounds good. Thanks for the advice that it's a long walk from the Metro to Gare Montparnasse.
When I get off the Eurostar, will it be obvious how to get to the Metro? are they in the same station or do I go outside?

Sarah, if you like apps then definitely download the Bonjour RATP app to your phone. It's an amazing tool to search the best way to get from one area to another using public transportation in Paris. Gives up to the minute times and is very accurate. We just used it for a week and it was terrific!

Or you could try citymapper which is also a great app for transit. It will even tell you which section of the metro will be best for your trip. Here is a very complete guide to Gare du Nord that will help you find Metro line 4: https://parisbytrain.com/gare-du-nord-photos/

I will be arriving Gare du Nord at 1645 unfortunately

Why unfortunately? Still before rush hour, which is more like 18.00-19.00 in Paris.
Gare Montparnasse will be busy with commuters but all in all you should be able to reach Chartres by 20.00 or so.

just to reinforce the message about the slog from the Métro into gare Montparnasse (and be sure you go to the correct section of the station - it is huge and spread into various sub-areas)

Thank you all so much!