It doesn't 'get on my jangly bits' as such, more makes me laugh and think "why the hell did you just do that, you moron?" You can pretty much see it on tv, whilst on holiday, freinds do it, it's great!
Here's a scenario:
Lost Tourist to french bloke (in perfect English): "Excuse me could you please tell me the way to the…………… (engage Allo Allo type ridiculous 'French accent') 'bus station'?
Now either add a "please" or if your feeling really French add a 's'il vous plaît' for extra effect. or say "Le Bus Station".
It's almost as if just by adding a daft accent, yet retaining your own language automatically makes the non-English speaking person think – "Oh silly me i was kicking myself for never having taken the time to learn English and i'm glad i didn't when all that is needed for me to understand them is for them to talk like René Artois"
You can witness this phenomena in Ross Kemp on gangs, foreign aid workers on the news and my mate Mike when speaking to his French girlfreind: "Catherine, would you like a cup of 'café'"
Just use the word 'coffee' Mike, i'm pretty sure she knows what you mean – you twit!