Advice on Rail Pass

First read this, a pass may be the wrong answer: https://www.seat61.com/Railpass-and-Eurail-pass-guide.htm#railpass-or-point-to-point-tickets

What may be a good idea is a Swiss Pass to cover the Swiss portion, and individual advance-purchased tickets fro France. A Swiss Pass includes the lake boats and buses, which are not included in multi-counry passes
For Swiss Passes, see here: https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests.html

For France, you will be way ahead to buy advance nonrefundable tickets for Basel to Paris. Could be as low as 36 EUR per person. A day round trip to Reims could also be done for about 22 EUR per person with advance nonrefundable tickets. Chartres and Giverny can be done with TER trains bought at the station and if off peak, you get a 25% discount.

What is your total time in Switzerland, how many different travel days are represented above, and what mountain trips will you also make that are not listed? All those factor into the choice of a pass, especially since the cheaper versions of the Swiss Travel Pass are for just 3 or 4 consecutive days. See https://www.ricksteves.com/travel-tips/transportation/trains/switzerland-rail-passes for the differences in coverage between that and a two-country Select Pass. [edited] Muerren to Schilthorn is again noted as fully covered in 2019 (when using a counted travel day) versus 25% off with Eurail passes (without using a counted travel day).

If you just get the Swiss Travel Pass, then buy your reserved Basel-Paris ticket in probably January to get the best rates. (With a Eurail pass, the seat reservation on this train is still rather expensive, maybe $30 in 2nd class.) Between Paris and Chartres or Giverny are cheap tickets to buy on short notice. Paris to Reims is again a faster, more expensive TGV, unless you purposely choose a slow train. See also https://www.ricksteves.com/travel-tips/transportation/trains/france-rail-passes.

For your travels:

Basel to Interlaken.
Interlaken to Lauterbrunnen.
Lauterbrunnen to Interlaken.
Interlaken to Basel.

Why not just skip Interlaken and use it only as a train transfer for your journey to Lauterbrunnen? Spend your nights in Lauterbrunnen or one of the other stunning alpine villages like Wengen or Murren? Yes lakes Thun and Brienz are very nice, but since Interlaken is only 20 minutes by train from Lauterbrunnen there's really no reason to stay in Interlaken.

If you must get a pass then the Swiss Half Fare Card usually always offers the biggest bang for your buck, but you'll have to do the math if you want the exact cost savings.

Thanks to all of you. I guess I wasn't very clear. Interlaken is listed only because I am guessing we will have to change trains there. We are staying in Lauterbrunnen 3 nights. I had thought we might take an early train from Basel to Interlaken, store luggage, do the boat trip (any recommendations on which lake?), then take the train on to Lauterbrunnen. During our time there we will explore Murren and Wengen. I knew about the change in the Swiss Pass no longer covering the trip up Schilthorn which is why I wondered if a Eurrail pass might be better. However, I like the idea of a Swiss Pass and then advance tickets on the other trips.

Any other tips for our 3 days in Switzerland? BTW, we are adding on the Switzerland/France trip at the end of a Viking cruise which ends in Basel.

Interlaken is listed only because I am guessing we will have to change trains there. We are staying in Lauterbrunnen 3 nights.

This is a common beginners mistake, thinking you have to treat each train separately. If you want to go from A to B (Basel to Lauterbrunnen or Lauterbrunnen to Paris), than that is what you need to look up on the train times website ( https://www.sbb.ch/en/ ). It will tell you where to change trains, which may be different places for different trains.
And, you just buy one ticket from A to B. NOT one per train. Except if you have a pass that covers only part of the route (for example a Swiss pass), then you need an extra ticket from the border station, which may or may not be where you have to change trains.

For your boat trip, I recommend the following.
Take an early train from Basel to Luzern, and do your boat trip there. There is left luggage at the station, and the boats leave from directly outside the station (not true for Interlaken).
From there, take a train to Lauterbrunnen. This route goes over the Brünig pass, and pass some lakes, and is scenic.

I don't know what time your boat disembarks in Basel, and you are only allowing 3 days for Switzerland, but I would recommend spending at least ½ day looking round Basel. It is a nice city. If you want to do a boat trip on your way to Lauterbrunnen as well as seeing Basel that would require a night in Basel, then an early train to Luzern.
Basel tourist info here: https://www.basel.com/en

Chris,

Thank you SO much for your input.

Our boat docks at about 1:00 a.m. I think. So I was planning on having breakfast and heading for the train station maybe around 8:30. I have been to Luzern and loved the lake and the city so your suggestion appeals to me. Certainly the ease of getting on the boat right outside the train station sounds good. Is it a tricky thing to do in Interlaken? We stayed in Interlaken before, but we rented bikes and rode next to Lake Brienz. I loved that! However, one in our group would not be a bike rider so I thought the boat cruise would be a better option. Would the boat in Luzern be significantly easier?

Also, if we have a Swiss Pass, it will cover the Swiss portion of our train ride to Paris, correct? Then if we are buying advance tickets for the rest of our train travel, can we get one just to cover the French portion?

A 4-day Swiss Travel Pass costs 270 CHF per person. I see that it will also be valid on the Schilthornbahn to the top in 2019. But you have to do the calculations to see if a Half Fare Card costing 120 CHF is a better deal.

There really is no pass that covers France. The TGV from Basel to Paris is an all reserved train, so even if you had a Eurail Pass, you would still have to purchase seat reservations to get on the train. These can be almost as expensive as just buying advance nonrefundable tickets. Same for the TGV to Reims and back. You really don't want to do this with local trains as it will take too long.

You don't have a problem buying nonrefundable airplane tickets to get to Europe and back. French TGV's operate on the same business model as airlines, which often they compete with.

Interlaken is between two lakes, Thunersee and Brienzersee (hence the name). The main station (Interlaken Ost) is between the two, and requires a long walk (30 minutes+) or a bus to get to either lake. There is more choice of boats at Luzern, and I think it is more spectacular.
Timetables are here: https://www.lakelucerne.ch/en/timetable-fares/timetable/
If you take the train from Luzern via Interlaken to Lauterbrunnen, you go along the side of the Brienzersee (and some other lakes), and you get good views. Click here for photo.

"if we have a Swiss Pass, it will cover the Swiss portion of our train ride to Paris, correct? Then if we are buying advance tickets for the rest of our train travel, can we get one just to cover the French portion?" - yes, correct. The border station, from which you have to buy tickets is usually Basel, but there are other routes, for example via Geneva.

Chris F, have they changed the Interlaken ship docks since July?

For years the dock for Thunersee (Lake Thun) has been about 10 metres from the tunnel under Interlaken West station, and the dock for Brienzersee (Lake Brienz) is about 15 metres or less from the tunnel under Interlaken Ost station.

Where are they now?

I've been lucky enough to have a BLS staff pass for Interlaken for the last nearly 20 years and have ridden them most years. I personally far prefer the Brienzersee because of the views, and being able to easily change to the train at Brienz, and most of all I really love the Giessbach experience. At Giessbach (the last stop from Interlaken Ost before Brienz, or the first stop towards Interlaken from Brienz) there is an ancient funicular railway up to the old Grand Hotel Giessbach in a beautiful location and fancy food and grounds, and the really great Giessbachfalle, the waterfall which comes down the cliff, through the woods and swooshes down to the lake next to the boat stage and the lower station of the funicular. I love it there.

That being said, after days on the boat making its way upstream to Basel do you want 2 or 3 hours on a lake boat?

With such a short amount of time in the Lauterbrunnen Valley that's where I'd spend my time. If you have time after that to want something else, then consider the boats. Plenty to do up the hill with 2 days and three nights that I wouldn't see Interlaken again until I was leaving.