The blasts underscore the major security challenges in Syria, where Macron is the first head of state of a major European Union country to visit since rebels led by Sharaa toppled Bashar al-Assad in 2024.
The explosions struck a busy area between the Syrian tourism ministry and the national museum across the street from the Four Seasons, where Macron was meeting civil society groups, Reuters reported.
Syria's state news agency reported that 18 people were injured in the explosions, including four police officers.
The first blast hit soon after Macron's motorcade left for the presidential palace. Reuters footage showed flames and smoke billowing from a trash can when a second explosion was caught on camera a few meters away.
The second blast went off next to an ambulance parked at the scene, where some two dozen people had gathered.
Flames and thick black smoke were seen billowing from close to the shops behind, as emergency personnel worked to put out the blaze.
Internal security forces have launched search operations to identify those responsible, Syria's state-run Al-Ekhbariya TV cited a security source as saying. Roads were sealed off and security measures were implemented after the blasts, a security source told Reuters.
Last week, a bomb at a Damascus cafe killed nine people and wounded 20 others. There was no claim of responsibility.