For optimal family fun, consider traveling between cities by train. The average journey time from Paris to Vienna is 10-11 hours, while the journey from Vienna to Salzburg is only around 3 hours. Depending on the season, you may wish to book tickets in advance to save costs.
Within each city, consider walking, biking or taking public transportation to get around.
Estimated transportation costs: Paris to Vienna by train (€103-€220), Vienna to Salzburg by train (€24-€65).
If you have more time in Paris, consider taking a day trip to Versailles or Mont Saint-Michel. In Vienna, exploring other palaces such as Belvedere or the Hofburg would be a great addition. And in Salzburg, visit the Red Bull Hangar 7 or take a day trip to the nearby town of Hallstatt to experience more of Austria's natural beauty.
If you have less time, consider skipping certain attractions or choose a shorter stay in one of the cities.