TGV tracks (technically called LGV = Lignes à grande vitesse) are the same as normal tracks, just better quality. Like the difference between freeway/motorway/autoroute and normal city streets. The LGV frequently end at the edge of cities (because it would be too expensive to build through urban areas). The TGV can run on the same tracks as other trains, provided the line is electrified. They run at normal speeds (which can still be 80-100mph) to the same city centre stations. This means at the city centre station you can change from a TGV to a local train, making the whole thing a connected network.
The TGV can also be extended well beyond the LGV, to provide a single service. For example Paris to Barcelona. If you look the LGV ends at Montpellier, and resumes again at Perpignan just before the Spanish border.
When you are leaving Paris Gare de Lyon (or Gare de Nord), you start on the same tracks as commuter trains, then on the edge of Paris there is a junction where the LGV starts. Then the trains starts to accelerate.