When I was in Paris last year I went into Hermes and was told there were no birkins but having read this threat I will wait until the afternoon so am planning a day trip to Paris in the next few weeks so will let you know how I get on. If anyone wants something specific and they have, I am happy to get it.
I just came back from Paris and as advised by Pinkish_love I went everyday last week and most of the days they had birkins.
You have to try everyday....you will find one. On Sat they had 4 black birkins plus others in stock.