Firstly taking rum, the French walk unsteadily (6)
I believe the answer is:
toddle
'walk unsteadily' is the definition.
(I've seen this before)
'firstly taking rum the french' is the wordplay.
'firstly' indicates taking the first letters.
'rum' becomes 'odd' (I've seen this before).
'the french' becomes 'le' ('the' in French).
The first letter of 'taking' is 't'.
't'+'odd'+'le'='TODDLE'
(Other definitions for toddle that I've seen before include "Walk unsteadily like a small child" , "Move like an infant?" , "Move like someone starting out on life" , "Walk like a young child" , "Aimless stroll" .)