Rail Europe does offer cheap, "non-flexible" TGV rates at least toward
Germany, Switzerland, and Italy. Within France or toward Spain, I
think I've only seen "semi-flexible," which is not the cheapest
category. For Paris-Munich direct on 5/13, for instance RE's price of
$55 is currently better than the DB price of €59.
That same fare shows up on the capitaine.com site for 5/13 at €45. The problem with Rail Europe is that they don't show all the lower-fare possibilities. The train arrives at 9:36pm. If saving money is you're most important goal, that's the train you take. But what if you'd like to arrive earlier in the day, even if it costs more? Rail Europe shows a total of 6 possibilities, all of which are $130 or more. Capitaine shows these same possibilities, but at fares as low as €69.
I checked the SNCF site for 5/13 and it also shows the €45 fare. DB doesn't show the €45 fare although it lists that departure time (at a higher price), but it does show the €69 fares.
I think what we're seeing here is the interaction of national systems. The €45 fare is on a direct train run by SNCF, so it shows up at that price on the SNCF website but not the DB site. The €69 fare for the trip leaving at 7:25am is on DB Bahn trains so doesn't show up on the SNCF website at that price.
The easiest solution seems to be to use a search engine that isn't tied to a train operator, such as capitaine. They show all the lowest fares with one search, regardless of operator.