The French high-speed rail system called the TGV for "Train à Grande Vitesse" is the best way to get long distances from city center to city center. The ease, convenience, and relaxation of traveling by train surely beats the brutality of flying. On the train, we often carry on a lunch and maybe a bottle of wine (yes, it is permitted) for a scenic and enjoyable journey.
The domestic French TGV routes are extensive. Centered in Paris, travelers can reach destinations like Nice, Strasbourg, Toulouse, and Tours in the Loire Valley. Travelers can travel to international destinations like Munich, Brussels, Zurich, and Milan on TGV or partner train lines. Here is a list of TGV routes. And of course, travelers can take travel under the English Channel to London on the Eurostar.
Other than the high-speed train system, there are extensive regional routes too. In general, regional trains do not require reservations and seats are unreserved although there are exceptions to this format. High-speed trains are reserved seating and should be reserved in advance, especially for holiday, weekend, and other peak travel periods. Purchasing in advance can afford price breaks too. It should noted that regional trains are generally not "slow" trains. For instance, we have been on regional trains that travel at speeds of 80 or 90 MPH where as TGV trains double those speeds.
It is always best to compare first and business class fares to coach fares, especially when purchasing in advance. Sometimes the difference in price is minimal but the advantages (larger seats and better services) can be great.
For us, the best place to purchase train tickets is on the website or app of Trainline despite the more well-known Eurail website. Trainline seems to have less fees and The Professor finds it easier to use in most cases. If purchasing tickets at the train station office, be prepared for long lines. There are electronic kiosks at almost all train stations to purchase tickets for faster service.
There are plenty of more detailed resources for finding out about the French railway system. The Professor recommends The Man in Seat 61 and there are many YouTube videos on TGV travel like this one.