Total will pay around €1.4 billion for the stake, based on €42/share.
Once the acquisition has been completed, it will then offer to buy the remaining shares quoted on the Euronext Paris exchange at the same price.
The offer values Direct Energie at approximately 12.5 times its provisional 2018 Ebitda (earnings before interest, taxes, depreciation and amortisation), Total said.
The move is part of the Group's strategy "to develop low-carbon energies, in line with our ambition to become a major responsible energy player," director general Patrick Pouyanné said.
Direct Energie, which bought French renewables developer-operator Quadran in 2017, brings with it an installed capacity of 1.35GW, including 550MW of renewables, and a pipeline of 2GW in France.
It had 368MW of installed wind power at the end of 2017.
Total is targeting at least 10GW of overall gas and renewables capacity in 2023.