The bank announced the deal in a joint statement but did not disclose the financial details.
Fidor, an entirely online-based bank that prides itself on completing all of its services in under 60 seconds, will remain independent after the takeover, which will help it address a funding squeeze, its chief executive said.
For BPCE, Frances second-largest banking group, the acquisition marks the move into digital services as more customers handle their business online.
Fidor was founded in 2009, one of the first German fintech companies, and now has 120,000 customers.
The German lender recently partnered with German telecoms operator Telefonica Deutschland to offer an online bank account that pays out interest to customers in the form of mobile phone data usage rather than cash.
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