Yes..its wrong bcoz you have to use a ellos or con ellos after encontramos.
If you wanted to use nosotros, that would be "Nosotros nos encontramos" - in this answer, nosotros is omitted because it's understood from the verb. "Nos" is needed either way, because it's the object of "encontrarse" here. The sentence translated exactly would be more "we found ourselves on the beach" but the way it's used is to meet up.
How do you get "meeting" from "We find ourselves on the beach." Is it just "We are on the beach."?
Answer. (Meet up on the beach) Only if we have been in the water or arrived by boat. Otherwise, we'll have to be content with meeting at, on, or down on the beach.
The translation above is not the example given to me. My answer was 'Shall we meet at the beach?' which was corrected to 'Will we meet at the beach?' which is actually wrong as the strictly correct form is 'shall' for I and we.
Strictly correct can be a matter of geography. According to my Oxford Practical English Usage grammar book, " Some British people use I shall and we shall instead of I/we will, with no difference in meaning in most situations... Shall is unusual in American English in most situations."
Shall should be accepted as well but will is correct in American English. Report it if you haven't already. Your fellow brits will thank you.