Taking off with a Parisian, travelling for free (10)

I believe the answer is:

unhitching

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'taking off' is the definition.
The definition and answer can be both to do with contact as well as being present participle verbs.
Maybe there's an association between them I don't understand?

'parisian travelling for free' is the wordplay.
'parisian travelling' becomes 'ing' (I am not sure about this - if you are sure you should believe this answer much more).
'for' is a charade indicator (letters next to each other) (I've seen this in other clues).
'free' becomes 'unhitch' (I've seen this before).
'ing' put after 'unhitch' is 'UNHITCHING'.

'with a' is the link.

Can you help me to learn more?

I've seen this clue in The Guardian.

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