A version of this story was published on 17 April when the companies agreed the deal. It was updated on 6 July.
Total has paid €42/share for a total consideration of around €1.4 billion for the stake.
Following the completion of the share acquisition, which was agreed in April, Total has now offered 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.