[quote=NarcolepticSailor]
I don't think it quite works that way. I mean look at Iraq and their army after everything the United States did. This would be on a much larger scale and would probably cost the both of you a great deal of money.
[/quote]
Iraq is a bit of a different story. This would be the equivalent of selling weapons to China and then China equipping themselves, not overthrowing its government and establishing a new one with new institutions and technology.

[quote=The Nexerus]
Turns out someone did, and it didn't make much of a difference. The RoC didn't last long.
[/quote]
Also not a relevant example. We have warlords, the Japanese, and the Soviets to thank for the failure of the Republic of China, not the integration of new technology. What would theoretically happen here is that Britain and France sell schematics to a more open-minded Qing Empire for it to strengthen itself. In fact, you could probably compare it to a Self-Strengthening Movement that has Qing's full support [i]and[/i] the support of foreign powers. In other words, it'd be a wildly successful version of what Qing tried to do in real life.