The most common and most likely answer to this crossword clue is the 4 plus 6 letter word LOVE LETTER
I've seen this crossword clue in The Daily Telegraph
L
O
V
E
L
E
T
T
E
R
More clues leading to the result LOVE LETTER
- O for some romantic correspondence!
- Affectionate note from landlord after nothing
- Missive to sweetheart with zero character?
- O Valentine!
- Duck landlady’s declaration of affection
- Private correspondence means nothing to the landlord
- Passion for landlord expressed in words
- Nothing against landlord’s romantic reading material
- Affectionate communication, nothing to be presented to landlord?
- Zero character shown in billet-doux
Buddy explains!

The straight part
We know that "billet-doux" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case billet-doux = love letter.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.