Dd1 is in the final year of a course at a French University (although she is registered in France, she's actually doing the year in a non-European country, but paying the French fees). For her it was about a specific course at a specific highly regarded uni, rather than just 'study somewhere abroad'. Her back-up plan was a course taught in English at Leiden in Holland. We're in Germany where Unis are largely free (you pay an admin fee of several hundred a semester), so both France and Holland seem more expensive for us - but of course they're both far cheaper than the UK. It means she'll be finishing her undergraduate studies with no debt, which is great.
When DD was thinking of Holland at 17, we bought her a plane ticket, booked her a youth hostel in Amsterdam, and sent her off alone for an open day/weekend. It was great to give her an idea of 'this is what you'll be dealing with by yourself if you choose to come here'.
DD's primary reason was NOT learning another language, and her course was taught in English, but a French class was compulsory and her French is now at C1 level, so it worked for that reason too.
The biggest issue your DS would face is that nobody yet has a scooby what the Brexit consequences will be, but he'd probably have to apply for a residence permit/visa to stay in any EU country, and that might involve demonstrating in advance that he can finance his studies.