transportation between paris train stations

Although part of the trip from Amboise to Paris may be on a regional train (TER) whose fares will not increase if you wait until you get to France to buy the tickets, you'll definitely want to take a TGV from Paris to Strasbourg. TGV fares can be bargains if you commit to a specific date and time and buy the (essentially non-refundable/non-changeable) ticket very early, or they can be much higher if you buy at the last minute. It's conceivable that a TGV might entirely sell out as well, though I don't know how common that is.

I've done the cross-town transfer in Paris, and it went well, but it's an experience I'd rather avoid, if possible. I checked the schedule for Monday and found a 9:38 AM departure from Amboise with a single change (to a TGV) at St-Pierre-des-Corps, arriving in Strasbourg at 2:21 PM. You'd have a 72-minute layover in St-Pierre-des-Corps, but the total time for this trip isn't any longer than the other options I saw. If you are traveling on a different day of the week, you may not have this option. Check SNCF.com for a date in, say, May that is the correct day of the week.

Edited to add: If you end up having to change stations in Paris, you can do a test booking on SNCF.com to see how much time it allows for the change. Click on the fare for the train you're iterested in, then on Journey details. If you have mobility issues or heavy luggage, the SNCF time allowance might not be long enough.

Acraven may have the best solution, avoiding Paris entirely, if it works with your schedule.

If you have to change stations in Paris, with luggage, the simplest choice would be a taxi. The least expensive would be Metro Line 4, in the direction of Porte de Clignancourt. My map shows 13 stops to Gare de l"Est. I expect the Metro would be faster but I don't really know. Depends on traffic, time of day, how long it takes to get between stations and Metro vs. taxi ranks, how long you have to wait for a taxi or Metro train. Some of our Parisian friends like Kim should have better knowledge about this.

The No 4 Metro line will get you there in matter of minutes. There is a rather long underground moving walkway that will cover part of the distance from the mainline train platforms at Montparnasse to the entrance to the No 4. Cost is 1.90 EUR per person for a single ride ticket.

I will be doing the same transfer across Paris again in September. I’m planning to take the metro. You don’t need to transfer across lines - just Line 4.

I have taken a cab across town from Montparnasse this year and it was totally bogged down in traffic. I was very glad I didn't have a train to catch. I would definitely take the metro.

I generally use the metro. I like getting off the street so I don't have to worry about surface traffic. Sometimes the walk is long and/or a transfer is required. If you have a lot of luggage, you may want to risk surface traffic to keep from lugging bags a long way.