I am not a native english speaker, sorry if my question is silly, but is it not either "at the crossroads" OR "at a crossroad"? It looks strange to me, an indefinite article with plural... :)
To me "at a crossroads" sounds more natural than "at a crossroad." Both are probably acceptable though. I've only ever really heard it in the figurative sense about having to make an important decision.
It's a weird-looking term for sure. I assure you "a crossroads" is the correct singular form though. If it helps, you could try to thing of it as a shortened version for "a crossing of roads" since it's a single junction of multiple roads.
By the way, "a crossroad" would be a single small road that crosses a bigger one. So it's definitely its own thing. English is wonky, I know. :)