Even a smart tax should be part of a low taxation burden

http://www.wsj.com/articles/should-the-u-s-adopt-a-value-added-tax-1456715703

In France taxation is too high and it is the main cause of low demand and further to deflation. In this setting it does not matter whether it is VAT or other taxes. French people haven't any cash in their pouches to buy stuff. That's all.
As a matter of facts when we compare GDP/hab ($) between France and Denmark; we get that from 96-00 to 2011-2015:

Denmark                                France  61,304.1                                43,807.5  57,636.1                                40,850.4  59,818.6                                42,627.7  60,718.4                                42,725.7

So France is poorer than Denmark and recovered poorly from the recession. A high taxation rate is associated with poor recovery and seems to impact more french demand.

Look at the trend to understand why demand is crashed by taxes:

"Europe’s experience

Take Europe, where the VAT is a major source of government revenue. When Belgium, France, Germany, Ireland, Italy and the Netherlands adopted a VAT—all between 1968 and 1971—their stated revenue goal was neutrality: Gains in revenue from the VAT were to be fully offset by reduced taxes elsewhere. (France already had a VAT but needed to revise it to meet European Economic Community Standards.) All failed. Government revenues—and spending—rose substantially as a percentage of GDP. In 1967 in France, the year before that country adopted its EEC-compliant VAT, total government revenues were 33.4% of GDP. In 1968, France adopted a VAT rate of 13.6%. By 2014, its VAT rate was 20% and government revenues were a whopping 45.2% of GDP. When Britain adopted a VAT, the government’s stated goal was to reduce revenue. That failed, too. Only one country, Denmark, adopted a VAT to increase revenues. It succeeded."