Is shenanigans from Irish shee nanna gasne or from French for `I dunno'?
[Although it sounds like a word of Irish origin] one source doesn't even mention a possible Irish origin, but instead, it indicates that Spanish chanada (a short form of charranada `trick, deceit') is a likely origin. William and Mary Morris (see the bibliography) note that shenanigans could come from Irish sionnachuighim `I play the fox.' But both the sources mention German dialectic schinageln `to work at hard labor' as a possible origin for shenanigans. Apparently, the implication is `using trickery to avoid hard labor.'
A French connection is unlikely.
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