Again, its like with Italy: the British and French were both extremely reluctant to give up their colonies, and there's very little chance of Ethiopia actually being able to provide something to both make their contribution worth it. And even if it was that they did make such a contribution, they have to actually have the power to make it so that either the French or British feel compelled to give something up, instead of simply proceeding to ignore their promises post war, just as they did to a far more powerful Italy. I can't see any such possibility.
On the other hand it isn't impossible that the French allow transit for Japanese goods through. The French in the 1930s had been passive before Japan in China during the first part of the decade, concerned about their relative weakness in the region, and rejected cooperation with the Anglo-Americans (at least this is my recollection from La France en Chine: 1843-1943, which to be fair I did read a year and a half ago and is a continent and an ocean away so I can hardly check it). A combination of coercion via threats against French interests in China, incentives with economic agreements (Japan and French Indochina had vigorous exchanges of Indochinese rice, coal, and I presume rubber in exchange for Japanese manufactured goods like textiles - some sort of alteration in their favor of the French is what I'd see as a possibility, but I am sure there are other, more direct routes), and crises in Franco-Italian relations which happened at several occasions, would probably be more than enough for the French to enable wide shipments of goods into Ethiopia. Historically the Germans sent arms to Ethiopia during the Italian-Ethiopian war which I can only presume had to be transported through the French railroad, it being the only route into the country, so therefor the French don't seem to have been particularly picky concerning it.