Distributed publicity material the French left during a fair day (9)
I believe the answer is:
leafleted
'distributed publicity material' is the definition.
(to leaflet is to distribute leaflets)
'the french left during a fair day' is the wordplay.
'the french' becomes 'le' ('the' in French).
'left' becomes 'l' (common abbreviation).
'during' means one lot of letters goes inside another.
'fair day' becomes 'feted' (I can't justify this - if you can you should give a lot more credence to this answer).
'a'+'feted'='afeted'
'l' placed inside 'afeted' is 'afleted'.
'le'+'afleted'='LEAFLETED'
(Another definition for leafleted that I've seen is " dropped fliers".)