The short answer is 'yes', and it has always had a hidden drink problem, but the problem has changed recently, and is much more openly discussed.
Alcoholism, liver disease and alcohol related cancers, heart disease and accidents appear to be significant killers in France, but nobody knows exactly how many people die of alcohol related causes every year, because the authorities have not standardised the data collected. The figure is probably somewhere between 30 000 and 50 000, with twice as many men as women dying of alcohol related causes, and nearly half of the deceased under 65. Alcohol related presentations at hospital Accident and Emergency clinics are definitely on the increase, as are hospital admissions due to alcohol related diseases (up 80% and 30% respectively in the last 5 years). I tried to get comparative figures from Australia, to give the French figures some context, but after a frustrating hour or so searching on the internet, it seems Australia does not present its statistics in the same way, so I can't compare apples with apples.
A friend of ours, who works in the wine industry, recently told us a story about going through the checkout at the supermarket with her weekly shop. A kid in his early to mid teens was in the queue behind her. He put his stuff down on the belt and both of them went through the checkout. What our friend hadn't realised is that he had surreptitiously put a bottle of wine amongst her purchases, which went through as hers and she paid for. As she was exiting the shopping centre the kid tapped her on the shoulder and said 'Excuse me, but you have my bottle of wine'. She tried to give him the benefit of the doubt by thinking that he had been sent by his mother for a bottle of cooking wine (it was in a plastic bottle and cost €2) but she is fairly sure that what he was actually doing was circumventing the possibility of being challenged about his age, and was just after some cheap alcohol for himself. She said it was extremely subtly done.