If intervention comes much earlier than 1864, then the US isn't in a good spot to eke out a clean victory. After that point, they probably have enough momentum to see the conflict through. British and French aid is likely going to be mostly in materiel and naval support, rather than boots on Confederate soil. In the end that doesn't solve the Confederacy's long term problems. The conflict probably quietly ends once the South surrenders. The US in unlikely to be in a position to punish the British or French for their actions and they probably feign an excuse to justify the intervention.
One interesting knock on effect would be a likely Anglo-American rivalry, especially in the Pacific. Oregon is already resolved, but Alaska and Hawaii might much more contentious acquisitions for the US. Russo-American relations might remain better for longer given the common geo-political enemy. Similarly Japan and the UK might maintain their relationship rather the UK dumping them for the US as in OTL. WW1 may not look particularly different, although the chance the US remaining neutral certainly goes up. For WW2 however, a Japan with a strong ties to Britain is probably less likely to go rogue. That might butterfly the whole Pacific theater of the war away, making it primarily a European war.