I got those figures from here: https://books.google.com/books?id=apKZDgAAQBAJ&pg=PA187&lpg=.... But maybe the French are overengineering? Entirely possible.

I see, thanks for the citation. It looks like those are numbers for a few actual railways—i.e. "On railway X, the maximum speed somewhere along the track is n, and the minimum radius of curvature is r." Explanations could be: (a) the path of the train didn't really need any sharper turns (i.e. "minimum allowable radius" ≠ "minimum radius we chose"); (b) different architects, working at different times, possibly using different materials, chose different safety margins; (c) perhaps one of the lines is designed to carry taller or heavier trains.

I do believe that, holding everything else constant, the minimum allowable radius would be proportional to the square of the velocity of the train. If you look at table 6.15 on page 183, it compares 250 km/h with 350 km/h, and 350/250 = 7/5, and (7/5)^2 = 49/25 = 1.96, so I would predict the radius would be roughly 2x for 350 as for 250, and, if you compare corresponding entries in the table, you see this holds very well for the columns labeled "(1)" and for the rightmost three columns, although those labeled "(2)" (apparently done with a different calculation—I can't see the page the calculation is from) diverge somewhat.