The proposal is part of a series France has made ahead of an EU summit next month that also includes a call to put in place new tax rules that would require non-European Internet companies to pay taxes in Europe on profits earned there.
France suggested studying "the introduction of tax rules for digital companies that would ensure that profits they generate in the European market are subject to taxation and the revenues shared among the member states," according to the document, obtained by AFP.
Complex, but legal, tax structures have allowed companies like Amazon and Google to pay little profit tax in most European countries although they generate hundreds of millions in profits in these markets.
A hot button issue given the austerity policies governments across Europe are implementing, British lawmakers recently gave Internet company executives rough rides in hearings over the tax avoidance schemes.
Through pricing of intellectual property companies can show most profit in European countries which have lower corporate tax rates, such as Ireland where Google has its European headquarters.
In a new proposal, France suggested "preparing a report on the possibility of taxing data transfers outside of Europe", but did not elaborate.
The transfer of personal data outside the EU is highly regulated in order to protect the rights of individuals.
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Both transfers of data inside companies, such as sending information on employees from a European subsidiary to a non-EU parent, and between companies are affected.
Transfer of personal data often happens when companies outsource certain tasks such as customer sales and help lines to offshore call centres.