'Milieux' seems to be working out OK. There's a grid position with letter 6 in the correct positions, so I=6. On that basis, I haven't yet found anything that doesn't work, but it will take a few minutes more to be sure.
Very well spotted, NACW. Chambers Dictionary does contain 'milieux' so technically it's allowable and they (Chambers) believe that it is a French word that has entered the English language.
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