Why can't I find any records for the Basque country on Ancestry.com?

Of course Spain had and has a records system, however don't think everything is online and certainly not all on one commercial website. Websites if you put every one of them together only have a tiny percentage of any countries real records, most are not online and many countries scan or transcribe their own records and do not sell any rights off to foreign websites like ancestry.com, so all they will have is the old IGI from the mormons which is not a record, they consist of copied, donated and collected information (and NOT checked) now called 'collections'.... so ANY 'record' that says 'collection' you know it is not real and only a clue of where/when to look for a real record
French local archives have scanned many of their records, they are online and free and that is where you will find scanned copies of French real records.

Spain Church records are the primary source for genealogical research in Spain, which is predominately Catholic. Civil registration began in 1870. Many of the church records have been filmed, but you have to write to the local Court of First Instance for the civil records The National Library of Spain http://www.bne.es/es/Inicio/index.html
The Basque country consists of three regions, each have their own records back approx 500 yrs

Basque country? There is no such thing, prior to 1970's. The Basque people lived in an area that is in Northern Spain and the records would have been maintained in the same manner as Spanish records. You might also try church records. Since you did not provide approximate years it is impossible to answer your question further.