The rail bed is even not that great, that's why only some ICEs are allowed on TGV routes, because they need a special deflector which is more robust to tolerate the stones which are thrown up in the air when the train drives over it.
I think they took this in consideration when they designed the latest iteration of the ICE.
If https://en.wikipedia.org/wiki/High-speed_rail_in_France is to be believed, the high speed lines for TGV are primarily but not exclusively used for TGV:
"LGVs are reserved primarily for TGVs. One reason for this is that line capacity is sharply reduced when trains of differing speeds are mixed, ..." "Some stretches of less-used LGV are routinely mixed-traffic, such as the Tours branch ..." "Outside France, LGV-type lines often carry non-TGV intercity traffic, often as a requirement of the initial funding commitments."
I'm also not so sure about the quality of the rail bed:
"Track alignment is more precise than on normal railway lines, and ballast is in a deeper-than-normal profile, resulting in increased load-bearing capacity and track stability. "