Re: Getting started in Switzerland
The LDS Family History Library has microfilmed records for Canton Jura.Here is what they have for the two villages you mentioned.If you go to familysearch.org you can get the location of the Family History Center nearest to you and go there to order the microfilms that cover the period of time in which your ancestor may have been in the area. You can also access the Family History Library Catalog on line at the familysearch.org site in order to get the film numbers that you need to order, or they can help you at your local center.
Asuel - Registres Paroissiaux Eglise Catholique, 1803-1873. For earlier records see Charmoille.
Asuel - Registres de l'État Civil, 1792-1815.For marriages 1798-1800 see Cornol
Asuel - See Ajoie (Seigneurie) [Manor of Ajoie] for early Guardianship and Probate Records
Asuel - See Alle for Manor of Ajoie Estate Records, 1461-1791
Courgenay - Registres Paroissiaux Eglise Catholique, 1641-1873.See *NOTE*
Courgenay - Registres de l'État Civil, 1792-1814.For marriages 1798-1800 see Cornol
Courgenay - Actes de Notaire, 1779-1814; 1783-1800; 1710-1730; 1595-1614 (Notarial Records)
Courgenay - See Ajoie (Seigneurie) [Manor of Ajoie] for early Probate Records
Courgenay - See Alle for Manor of Ajoie Estate Records, 1461-1791
Good luck in your search.