For a Russian citizen:
If I have a general purpose (6 months) visa for the UK, and am currently in the UK, does that make it easier to get a visa for France.
For example: I'm in the UK on the general purpose visa for a 3 month holiday, and I would like to visit Paris. So if I wander into the French embassy in London are they likely to give a French visa easily on the basis that I already jumped through all the hoops for the UK visa?
In short, no. Remember, you're dealing with a bunch of government bureaucrats here, you'll still need to satisfy every item on their checklist.
That said, having evidence of previous travel and (the important part!) having returned home will be helpful in proving that you're not planning to migrate to the EU permanently. However, I don't think you'll be able to apply while still in the UK, since the French only let UK residents apply for visas in the UK.
The good news is that obtaining a Schengen visa is relatively easy compared to getting a UK visa: lower application fees, shorter application forms, less supporting documentation needed, more locations where one may apply (VFS global offices in 15+ cities, if you apply from Russia), a straightforward application process, shorter processing times.
