Fashoda Incident would be your best PoD, I'm thinking. Let's say the De Bonchamps Expedition makes to Fashoda on time and meets up with Jean-Baptiste Marchand's force, making Marchand much less willing to compromise with the British. When Kitchener arrives, the two colonial forces come to blows, likely with the French losing. Tensions rise, but war doesn't occur--the French remain bitter. Eventually a war?
I'm just spitballing, but I think that might be a good idea.