The Energy Consumers Commission (ECC) insisted more work was required to "quantify the impacts of the energy transition".
It argued consumers need more information about steps to reduce emissions.
The gilets jaunes or yellow vests movement, which swept across France in 2018, was initially sparked by a planned rise in the tax on diesel and petrol.
It later grew into a wider anti-government protest and saw violence erupt on the streets of Paris and elsewhere.
The protests have been linked to deaths and serious injuries, as well as thousands of arrests.
The ECC was formed in July last year following a Scottish Government commitment to enhance the voice of consumers. Its membership includes academics, local groups and bodies such as Citizens Advice Scotland.
In a briefing, it said: "Ensuring equity is built into Scotland’s net-zero transition is one way of minimising the risk of backlash against decarbonisation activity and progress stalling, as was seen with the gilets jaunes protests in France.
"More work is required to quantify the impacts of the energy transition and to design and implement mitigating interventions."
Scotland has committed to becoming net zero by 2045.
But the ECC insisted that while concern around climate change had never been higher, consumers needed more information.
It said Scots were making low-impact ‘social norm’ type changes to their behaviour, such as recycling domestic waste, but there was less evidence of high-impact changes such as the adoption of heat pumps or electric vehicles.
The commission said people needed more information about how low-carbon heating systems worked and the scale of the challenge around decarbonisation.
It said upfront costs were often cited as the main barrier to engagement with low-carbon technology, particularly in domestic heating and transport.
The ECC noted: “Changing consumer behaviour is a vital part of rethinking ingrained consumer patterns around domestic energy and transport.
"Such behaviours are often linked to beliefs about safety, health, status and personal liberty, which may explain why incentives that rely on rational decision-making have had mixed success.”
The commission warned tenants, low-income households, and remote and island communities are particularly at risk of an unfair transition.
Lewis Shand Smith, chair of the ECC, said: “With COP26 still clear in our memory, support for tackling climate change has never been higher in the public consciousness, but consumers remain unsure of what the impact will be on their everyday lives.
"People are taking steps towards doing their bit, but they are often relatively low-impact changes such as recycling.
"In reality we will need much larger use of low-carbon heating in people’s homes if we are to meet net-zero emissions by 2045, but consumers are uncertain about what that means for them, citing concerns over upfront costs as a serious barrier to engagement.
"A good first step in improving this engagement is to accelerate the roll-out and better communicate the positive effects of smart meters.
"These can be the first step consumers take on their own personal journey to more energy efficient heating in their homes.”
The Scottish Government has been approached for comment.