It's not correct that Basque is the only non-Indo-European language in Europe; this is also true of Hungarian, Finnish, Estonian, and some other minority languages in the far north of Scandinavia. However, it has been hypothesized that Basque is the only language in Europe that is pre-Indo-European, having existed there before Indo-European languages spread to that area (although it's hard to know this for sure). Either way, you're right that it's a fascinating language!