In my experience, likelihood of a transit is directly related to how competent you sound when asking. Fluff your lines, and you'll be told to remain clear of controlled airspace!
In addition to the above mentioned sites, Brize Norton are unfailingly helpful and will always let you through if they can.
On this side of the channel (the sunny, South side
), half the controlled airspace seems to become uncontrolled at weekends and at lunchtime - which makes life much simpler! When they're open, though, the same applies - ask nicely and they'll let you through. I've never been refused a transit through Lyon's zone, and on occasion have been routed overhead Lyon airport, which is the busiest regional airport in France.