Paris to Barcelona is best done by overnight train. Look for a cheap flight if you don’t like couchettes or T 4’s as more luxurious accommodations are expensive. The fastest day train is 7 1/2 hours and most options are around 12 hours. Use http://reiseauskunft… for train schedules anywhere in Europe.

Barcelona to Florence Would be a nightmare by train — 16 to 24 hours. Look for a cheap flight or possibly overnight ferry to Genoa and then train (ferry probably only runs in summer.). Even a cheap flight will easily kill a day on this trek as the airport many of the low fare airlines use is at least 90 minutes by bus from Barcelona.