The most critical lesson the U.S. can learn from either of them is not technology it’s how to get things done, at least within a normal human lifetime, and making it work reliably. Those capabilities are no longer in the American DNA. (Remember the saying good ol’ American know-how? Now it’s about keeping things from happening.)
Both the first Shinkansen and the first TGV were several decades in the making, decades during which they saw steps forward but also reversals of fortune. In the case of France this included several changes of government and swings between different political philosophies on the role and responsibilities of the state vs the private sector. In France the TGV was during its project stage furthermore competing head on against the Aerotrain, basically a fuel guzzling cross between a hovercraft and a monorail that was so insane that I'm sure Elon Musk would have supported it. And ironically in France too, the Aerotrain's main proponents came from the center-right side of the political spectrum (supported by the aerospace and defense industries) whereas the left preferred the TGV (supported by the rail industry). Yet in a great show of bipartisan pragmatism, and following up on prolonged indecision by left wing governments, it was a center right government that took the jump and committed the funds and launched the construction of the initial TGV line (thus pulling the plug on Aerotrain).
The earlier proposals for the TGV project were also quite different to what was finally delivered. For example the prototype train used gas turbines rather than electric traction. The oil crisis caused a re-think there. The TGV would never have become a thing if there had not been individuals both in government and in SNCF management who effectively put their careers and necks on the line by standing behind something that, had things not worked out as well as they did, would have destroyed their reputations and left them looking like snake oil salesmen.
In the perspective of history it is easy to look back and think, it was all so simple and they were following the logical course of action. But this was far from obvious at the time. It is this this type of visionary individual we need again, who can champion the project even across changing administrations and political directions.
The Japanese project went back even further, to pre-war proposals for a new faster rail system, which again had very little in common with what was finally built.
So it's maybe misleading to assume these things happened linearly or smoothly, and maybe the passage of time helps one forget some of the battles that had to be fought, and the near defeats that had to be survived.
Also, both projects served political purposes. France was recovering from a post war slump and re-emerging as a leading industrial nation, or at least trying to project this message to the world. Projects such as the TGV and the Concorde helped push that message, and no doubt also helped French industry get onto people's radars. Although the TGV itself was only moderately successful on the export market, French industry pushed large volumes of metros, freight locos and such, possibly on the back of the TGV's fame, including many exports to countries normally outside of France's normal sphere of influence. The Japanese were also interested in export, which was one of the reasons why they chose to go for standard gauge. Similarly to the French, they did not have any immediate export successes for the Shinkansen but managed to sell a lot of other stuff.
The TGV was by nature more complex than the Shinkansen, due to the need to be reverse compatible to the legacy rail network and islands of 1500V DC electrification, plus the need being recognized from the decision to go electric, to also provide for compatibility for 16.7Hz for international services. A feature that was not to be used on a significant scale until many years after. Not to forget the hotchpotch of incompatible legacy signaling systems that a TGV must deal with, especially the international ones.
Texas Central will be a standalone system that does not need to be compatible to anything else. This should hopefully simplify many decisions.