The most common and most likely answer to this crossword clue is the 5 letter word LOIRE
I've seen this crossword clue in Independent
L
O
I
R
E
More clues leading to the result LOIRE
- Water flowing round among coins once thrown in Trevi?
- Old Italian bread around duck in river
- Behold fire beginning to be put out — there's flowingwater here
- French river, one embodied in folk tradition
- French river, one in mythology
- Knowledge from long ago about one European river
- Learning to conserve one foreign flower
- Collective wisdom about one French river
- Collective knowledge about island river
- Accumulated facts about current in European river
Buddy explains!

The straight part
We know that "continental river" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case continental river = loire.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.