Old French president concealing origins of affaire involving starlet: sauce! (11)

I believe the answer is:

hollandaise

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'sauce' is the definition.
(I know that hollandaise is a type of sauce)

'old french president concealing origins of affaire involving starlet' is the wordplay.
'old french president' becomes 'hollande' (I can't explain this - if you can you should believe this answer much more).
'concealing' indicates putting letters inside.
'origins of' says to take the initial letters.
The first letters of 'affaire involving starlet' is 'ais'.
'hollande' going around 'ais' is 'HOLLANDAISE'.

Can you help me to learn more?

(Other definitions for hollandaise that I've seen before include "Sauce to go with fish" , "Sauce used with fish" , "Rich sauce" , "Sauce, eg for asparagus" .)

I've seen this clue in The Everyman puzzle in The Observer.

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