Hey !
it actaully depends on how long you are staying in France and where you are arriving. i suppose you are first staying in Paris. just to tell you that from Paris you can get very fast most of the places in France by train, but from one city to an other it can be very difficult sometimes, so be carefull...
if you want to stay in a sunny and warm place you can go down to Bordeaux (3 hours TGV), and continue to nices places as the "student city" Toulouse (cheap easyjet flights from paris), or further south to the basque country (surfing place Biarritz, st jean de Luz etc.), and from there you are very close to the spanish basque country (charmfull cities like san sebastian, Bilbao).
an other place for sun is of course the Rhône valley and côte d'azur, you can get to Lyon (nice but busy, 2 hrs tgv), Grenoble (Alps) or Montpellier, aix en provence, nîme or valence (about 3hrs tgv, quite close to each other), for côte dazur it is nice to go to Grasse, St tropez (jet set), Nice, Monaco (just to see the millionairs 😉 )
for more germanic places you can go the really wonderfull city of Strasbourg (4hrs30 by train, no tgv), and maybe continue your trip to Freiburg and Munich, Germany (Baviaria) or join the south of France by train (certainly quite long ...)
and an other route could be to the north like visiting typical flandrian city Lille (1hrs TGV), continue to London (1hrs30 from lille by eurostar), or to Brussels (20 min from lille), Brugges (certainly one of europes most beautiful city) and have a bit of fun in Amsterdam ...(3 hrs from brussels, train)
ok, i dont know exactly what you are looking for, if it is more like little typical french cities you looking for you can travel to Normandy and Brittany, where it is raelly french ! the musts there are Rouen, Honfleur, Caen (famous because of world war 2), Mont st michel (the must of the musts! but no train ...), St Malo, Rennes, Le Mans, and Nantes.
and if you are in Paris and wants to make a kind of "daytrip" you can go to champagne city "Reims" (NE, 1h30 by train), or to Dijon (1h30 by TGV), Chartes (1h30, train, famous for the cathedral), Rouen (1h30), Le mans (1hr TGV).
So you got the choice now ... there is a lot to see, I can just tell you that Lille, Paris, Strasbourg are my favourite places, and Rennes, Montpellier, Toulouse, Bordeaux, Nanttes certainly have the best reputation ...
and try on "easyjet.com" (and not Ryan air = shit), you can find very interesting fares from Paris to great places in Europe (Pisa, Barcelona, Madrid, Nice, Rome, Berlin ...) I just went to Pisa & florence for 50 return !
Have fun ! where are you actually from ?
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