Sorry, but this would never happen. Russia has absolutely no ability to take possession of the French territories in Asia, even if the French made no effort whatsoever to defend them (which they obviously would). Besides which, Russia was dealing with a major uprising in Poland during the American Civil War and was trying to stay on good terms with the French to make sure they didn't throw their support to the rebels. The last thing Russia would want in the 1860s is a conflict with France.
As for the United States "owing" Russia for its aid, what on Earth can the United States offer that would be of the slightest benefit to Russia?