Judging from my own behavior as a rather lazy consumer and from observing the people around me, it seems to have been pretty effective. Most of the people around me bring a bag to the store and personally I buy many fewer 10c bags these days.
Starting with the fact that Europe is much less car focused, which leads to more trips with smaller amounts being bought each time. The more condensed European cities lend themselves to that kind of behaviour, since the trips are going to be pretty short and likely to be made on a bike, walking, or using public transport.
From my experience, I would estimate maybe 20% of checkouts include a 10c bag, the rest just use their own backpacks, cotton bags or the reusable sturdy kind of plastic bags. I don't even know when I last saw someone buy multiple 10c bags to carry their groceries.
AFAIK, you still can get free plastic bags if they are part of necessary packaging, for example on farmer's markets.
EU Directive: http://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CELE... says:
"Member States may choose to exempt plastic carrier bags with a wall thickness below 15 microns (‘very lightweight plastic carrier bags’) provided as primary packaging for loose food when required for hygiene purposes or when their use helps prevent food wastage."