I disagree re: density, Gasmon.
Paris - Lyon is a very well traveled rail line, and that city-pair is not too much larger than Dallas - Houston (15 million vs. 11 million, respectively), which generates about 5,500 passengers to/fro via short-haul flights daily. The distance traveled between Dallas and Houston is about 220 miles, easily within the optimal range of high-speed rail. The 5,500 shuffling between Dallas and Houston merits about 10 fully-loaded duplex TGVs per day, to say nothing of supplanting some of the vehicular traffic between the two cities. I would easily say that 15-20 trains could traverse the line, if built, or about one per hour or two during peak times.
Other city-pairs within the South Central Region, and their current airline passenger figures to/fro:
I-35 trunk line - south - 270 miles in distance
Dallas - San Antonio (8 million combined) - 270 miles apart - 2,100 passengers daily +
Dallas - Austin (8 million combined) - 190 miles apart - 2,000 passengers daily
I-35 trunk line - north - 550 miles in distance
Dallas - Oklahoma City (7.5 million combined) - 210 miles apart - 600 passengers daily +
Dallas - Tulsa (7.5 million combined) - 270 miles apart - 1,100 passengers daily +
Dallas - Kansas City (8 million combined) - 550 miles apart - 1,100 passengers daily
I-10/US 290 trunk line - 250 miles in distance
Houston - San Antonio (7 million combined) - 250 miles apart - 1,000 passengers daily
Houston - Austin (7 million combined) - 180 miles apart - 1,000 passengers daily
...
And, now, for no particular reason, some sexy eye candy:
