I think the first question to be addressed is what is the basis for him having been born in Freyburg?
There are cases of people relocation from Germany in the Austrian Empire—parts of my family did this (but earlier in the 1800s), but I have family records and documents that link the family in Moravia to an origin in Brandenburg.
It may be possible that your ancestor was not born in Karlsbad, but in a town/village very near there. This means identifying the towns and looking through all the church registers. There are no comprehensive indices, so this means potentially quite a bit of work. Records could be in Czech, German, or Latin (more common for older records, not those of the later 1800s).
As Colleen noted, there are extensive Czech records online from the Czech Regional Archives. These archives typically have much more than FamilySearch.
Membership in GenTeam May be helpful. This is a website for research in Austria and the Austrian Empire. Membership is required, but it is free. The website has an English version. It has a very useful gazetteer that has place names in both German and English, as well as links to the regional archives for each town.