"Estonia refused to continue [to cooperate] with us," Sapin told reporters.
The idea of the tax was initially suggested by Germany and France at the height of the eurozone debt crisis.
The proposal was later supported by Austria, Belgium, Italy, Spain, Greece, Portugal, Slovenia, Slovakia and Estonia.
The draft FTT directive suggests minimum tax rates in transactions between the state parties' financial institutions, with 0.1 percent on shares and bonds and 0.01 percent on derivatives.
According to the European Commission’s preliminary estimates, the financial transaction tax could generate the annual revenue of some 57 billion euros ($61.6 billion) for the bloc’s budget.