As of Friday, 80,000 French citizens had been vaccinated against the coronavirus so far. In comparison, neighboring Germany has done hundreds of thousands of inoculations.
The success or failure in vaccinating the population will likely shape the political debate as the campaign for the 2022 presidential race heats up in the coming months.
"Although the 2022 presidential election still seems a long way off, President Macron is certainly worried that a poorly-executed vaccine rollout now will harm his chances of winning another term," Jessica Hinds, a European economist at Capital Economics, told CNBC on Thursday.
Macron stood neck-a-neck with far-right leader Marine Le Pen in an opinion poll published in October.
The French president has reportedly complained that the pace of inoculations was "not worthy of the moment or of the French people" and said the situation "must change quickly and notably," Le Journal du Dimanche reported earlier this month. The president's office was not immediately available for comment when contacted by CNBC on Monday.
"A slow pace of vaccination would limit the government's ability to lift restrictions that are taking their toll on the economy and people's daily lives. This would clearly be unpopular among (French) voters, particularly if other countries such as Germany are able to remove them sooner," Hinds said.
Red tape has been the main reason for the delays. Citizens have had to get a pre-vaccination consultation and get consent from their doctor before a jab.
"What I find striking about the French strategy is that public officials did not pay much attention to logistics, to the nitty-gritty," Jeremy Ghez, Professor at H.E.C. Paris Business School, told CNBC via email.
Reports from the country also suggest there is high anti-vaccine sentiment across the population, when compared to other nations.
France's Health Minister Olivier Veran initially suggested that the careful distribution was taking into account the concerns regarding the vaccine among the general population. An Ipsos poll published in late December showed that only 40% of French people had plans to get the coronavirus vaccine.
But the French government now wants to reverse the situation by simplifying the process. France's Veran said that people aged 75 and over will be able to make an appointment on the internet or by phone in order to be vaccinated.
The country is also extending the criteria for eligibility and the government has vowed that 1 million people will be vaccinated before the end of the month.
France has been one of the hardest hit nations by the pandemic. Prime Minister Jean Castex said Thursday that restaurants and ski resorts will remain closed until at least mid-February and the nightly curfew will be extended until late January.
The social restrictions are taking a toll on the economy. France's GDP is expected to have contracted by more than 9% during 2020.
The slower the vaccine rollout is, the longer parts of the economy will remain shut.
"The French economy is under anaesthesia and it's only when you pull the fiscal plug that you will truly know how quickly economic actors can rebound. If this happens quickly, I like Macron's chances because there are so few alternatives as of today. If it does not, I would argue that all bets are off," Ghez said on how the economic performance will influence the presidential vote.
Macron defeated Le Pen in 2017 on a pro-EU agenda.