Well, wanting to be flexible with dates kind of disqualifies from the race cheap discounted tickets, which most of the time should be bought in advance & valid only for specific train & date. The options that are left then is either buying before departure or going with rail pass. Anyhow, let's take a look at each leg (all fares are for 2nd class):
Amsterdam to Ypres: neither TGV (mainly French Railways trains), nor ICE (mainly Germany Railways trains) is an option here.
Dutch Railways will sell you ticket for regular (InterCity trains) to Ieper for 59,60 per person, journey with two changes (Rotterdam & Antwerp) will take about four and a half hours. In case you want to travel faster (about an hour), then you can always go for high-speed Thalys train (on part from Amsterdam to Antwerp), however it increases ticket fare to 79,50 euro per person. Kind of expensive, especially taking into consideration that discounted tickets for Thalys start from 29 euro (if bought in advance) + another 17 euro for Brussels-Ypres leg
Ypres to Strasbourg: most logical route here is Ypres to Lille and then (using TGV train) to Strasbourg. Ypres to Lille is about hour and a half with one change in Kortrijk,
standard ticket cost 14,60 euro per person. With Lille to Strasbourg (3:20-3:50 depending on departure) things get complicated, because
French Railways (SNCF) to get the best fare you'll need to book well in advance, while flexibility will cost you about 100 euro per passenger here.
Strasbourg to Geneva: for those who don't want to purchase ticket in advance things are looking much better here, mainly because you can get (either via already mentioned French Railways website or at the ticket counter) relatively cheap regional (TER) train from Strasbourg to Basel first (24,10 euro per person, about 1:20 min.) and then travel with Swiss Railways, which has good option called
SuperSaver ticket (can be purchased even before departure) for 37,60-45 CHF (standard full fare ticket here is 75 CHF per person)
Geneva to Lyon: probably easiest trip, since it's rather short (slightly less than 2 hours) and there is relatively cheap direct regional trains (TER) for 28 euro/31 CHF
Cahors to Paris: no TGV here, but you have direct InterCites trains making a journey in about 5:30 (flexible fare is close to 80 euro, but discounted tickets run for twice as cheap and, surprisingly,
available even for some trains as soon as tomorrow)
Now about rail pass option... if we calculate sum total for flexible tickets mentioned above it all adds up to about 300-370 euro per person (60 euro for Amsterdam to Ypres, another 115 euro for Ypres-Lille-Strasbourg, then 24 euro to Basel, 35/70 euro (SuperSaver/standard flexible) Basel-Geneva, 28 euro Geneva-Lyon & Cahors-Paris 38/79 (discounted/standard flexible) euro.
Eurail pass for Benelux-France-Switzerland (5 travel days within 2 months + 1 free travel day) will cost you 329 euro (658 euro for both of you) and essential bonus here is that it's for the travel in 1st class, not 2nd. The only compulsory reservations you'll encounter is TGV Lille-Strasbourg & InterCites Cahors-Paris, both 9 euro per leg. This is pretty much it in case you can't/don't want to tie yourself to discounted non-exchangeable/non-refundable tickets
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