Most popular Jura crossings into Switzerland:
Champagnole - Morez - St-Cergue (view point) - Nyon/Prangins (National Museum) - Geneva/Lausanne
Pontarlier - Vallorbe (caves/iron museum) - Yverdon/Lausanne
Pontarlier - L'Auberson (Baud Museum) - Ste-Croix (view point, Cima museum) - Yverdon
Pontarlier - Travers - Neuchatel
Morteau - Le Locle (underground mills, Saut-du-Doubs waterfall, watch museum) - La Chaux-de-Fonds (watchmaking museum) - Vue des Alpes (view point) - Neuchatel
Baume-les-Dames - Audincourt (20ths century concrete church built by Navarina) - Blamont - Reclere caves - Ste-Ursanne (tiny medieval town) - Delemont
If you want to go to Zermatt, it's easier to take a border crossing leading to Lausanne, unless you will come from the Eastern part of the French Jura.
For all other questions have a look at http://www.myswitzerland.com/en/home.html and the many links you will find there
