Difference between research and résearch (with an accented e)

I suspect Wilson was using the accent mark as a stress indicator. The implied context, I believe, is that there had been a time when the noun "research" was normally stressed on the second syllable. Over some period of time before 1931 (the year in which Wilson wrote this), people began stressing the word on the first syllable. It's like referring, today, to someone "who lived in the days before dungarees had become jeans and pocketbooks had become purses".

'Résearch' is a nonce word created specifically for that one occasion to communicate a new idea. Sometimes nonce words become neologisms and become used by others. Sometimes not.

The accent on the 'e' is not a native English spelling. It is presumably intended by the author to change the more modest sounding 'research', to give the feel of a French word, which in English writing has a connotation of higher class or fanciness or highborn.

Searching google books for occurrences of 'résearch' finds nothing:

Likewise, searching French sources finds no evidence of a French word. The actual French translation of 'research' is 'recherches'.

Just because google ngrams doesn't find anything doesn't mean it doesn't exist (it's not searching web pages). But it's a good indication that it is either rare or not accepted by most people as a repeatable word.