but without this approval it would not be,is my take.

French term (edited): association agréée

regarding taxation

You might do better to replace 'I' or 'we' with the name of the company for example, to make it sound more impersonal / third person.

"As a member of an approved body, Dr X is in a position / able to accept payments by cheque"

I don't understand why you want to translate it. It is a Franco-French thing regarding French tax law, etc. that is probably meaningless even in Belgium, Switzerland, or Canada.

I see no point in translating "association agréée" since what you would really need is a to give your readership a crash course on the French business mentality, the meaning of "profession libérale", and tout le tralala.

As for accepting cheques, as you say, that's obvious. Only in France, where tax evasion and non-declaration of revenue is national sport, would it be necessary to remind people that you might, actually, take cheques (as opposed to cash in hand and mum's the word).

If it's to go on your or anyone else's stationery for overseas consumption, I'd simply delete it.

Short of adding a half-page footnote explaining what's behind the phrase, this would seem to be enough for the purposes of your text. I feel it might sound odd to people unfamiliar with the association agréée system to link membership of an 'approved body' with the ability to accept payment by cheque, since most people would accept that form of payment anyway!