SPIE's withdrawal leaves three candidates still in the running, Bouygues, Eiffage and Bain Capital.
SPIE, which had submitted a non-binding offer for Equans on Sept. 6, had been selected to participate in the due diligence phase.
SPIE "considers that the information made available as part of this ongoing due diligence phase is not sufficient to allow the company to prepare, within the defined timeframe, a binding offer that meets its standards and objectives," SPIE said in a statement.
"As a consequence, and despite the strategic rationale of the project, SPIE decided to stop all related workstreams and will not submit any offer at the end of this due diligence phase."
Equans provides energy and facilities management services to client companies and employs around 40% of Engie's total workforce worldwide.
The value of the deal is estimated at around 5 billion to 6 billion euros, sources close to the deal have said.
(Reporting by Dominique Vidalon; Editing by Chris Reese and Jane Merriman)