Some places, it is true, use different track gauges (eg. Ireland, Iberia and Russia), but Britain uses just the same standard gauge tracks as are the norm in every country where TGV trains regularly operate. And Eurostar trains happily use just the same tracks as any other TGV.

No, the Eurostar does not use a different track gauge; it runs on the Standard Gauge of 1,435 mm (1.435 m), which is the same width used by the national rail networks in the United Kingdom, France, Belgium, and the Netherlands. However, the Eurostar trains are built to a different "Loading Gauge." In railway terms, the loading gauge refers to the maximum height and width of the train cars themselves. Because older British tunnels and platforms were built smaller than their continental European counterparts, Eurostar trains (like the Class 373 and the newer e320) had to be designed with a slimmer profile to fit the UK's more restrictive infrastructure. This is why a Eurostar train may feel slightly narrower inside than a standard French TGV. While the tracks are the same distance apart, the "envelope" through which the train moves is smaller in Britain, requiring the Eurostar to be a specialized hybrid of UK and European engineering standards.