That is just the TGV map- they do have other services, though I'm not so sure as to their extent.
It would be nice if the map though showed which parts of those routes are on LGV and which parts Lignes Classiques
On this map the blue lines are the actual dedicated high speed new build lines:
http://upload.wikimedia.org/wikipedia/commons/thumb/5/57/Carte_TGV.svg/568px-Carte_TGV.svg.png
Briefly, essentially the dedicated new-build high speed lines are (in rough chronological order:
LGV Sud-Est
Original LGV Sud-Est: Paris - Sathonay-Rillieux (Lyon suburbs)
Sud-Est Lyon by-pass extensions: jct off original Lyon line - Valence TGV – south of Valence.
plus various short branches to link old to new lines (eg Aisy - Pasilly which allows TGVs to get onto the classic Paris - Dijon main line)
LGV Atlantique
Paris Montparnasse (uses reused alignment of a never completed railway to Chartres) then to Courtalain (southwest of Chartres) where it splits to go to Le Mans and Tours (just south of)
LGV Nord
Paris (Gonesse) – Lille (Fretin triangle) – Calais – Channel Tunnel and Fretin – Belgian border
LGV Jonction
Links LGV Nord and LGV Sud Est via Marne la Vallee
LGV Mediterannee
Runs off Lyon by-pass and down the Rhone valley corridor then splits, on branch goes to just short of Nimes and one to just short of Marseille
LGV Est
Paris suburbs – Baudrécourt (near Metz and Nancy). Second phase onto Strasbourg now under construction
LGV Rhin Rhone
Phase 1 opens December:
Villers-les-Pots (near Dijon) - Petit Croix (Belfort): 140 Km