It can happen regardless of who you're talking to (or not). Coming back from France last Thursday, we were talking to Lille Approach and at FL45 routing LT direct DVR. We heard another aircraft call him, 5000 feet QNH, routing Cap Gris Nez to LYD. Both aircraft were squawking.
We were surprised at his using QNH, so kept a good look-out and saw a bright yellow aircraft crossing right to left in front of us. We turned right and went well behind him. I don't think he even saw us.
Lille said nothing (we were VFR, after all). If we hadn't turned, we'd have got very close to the other aircraft.
What is the transition altitude the French side of the channel? I can't find it in my Bottlang, but have always assumed it's 3000 feet.