They say there are plausible biological mechanisms, such as the effect of sugar on the visceral fat stored around vital organs such as the liver and pancreas, blood sugar levels and inflammatory markers, all of which are linked to increased cancer risk.
After a nine-year period, it was noted that a 100-milliliter (3.4-fluid ounce) daily increase of sugar-based drinks led to an 18% increase in the risk of contracting cancer.
However, until now it has been hard to tease out the extent to which sugary fruit juices and fizzy drinks also increase the risk of cancer per se.
Drinks and fruit juices sweetened by sugar have the same increased risk also.
For every extra 100ml per day consumed on top of this, a person's cancer risk increased by 18% for all cancers and, among women, by 22% for breast cancer.
"This large, well-designed study adds to the existing evidence that consumption of sugary drinks may be associated with increased risk of some cancers", Graham Wheeler, from Cancer Research UK said.
Catherine Collins, an NHS dietitian, said the "take home message is the absence of cancer risk in using diet drinks containing artificial sweeteners". Sugary drinks such as colas, lemonade and energy drinks have been linked to obesity, which is a cause of cancer, but the French researchers suggest there could also be other reasons sugar could trigger it.
"The results indicate statistically significant correlations between the consumption of sugar-sweetened drinks and risk of all cancers combined, and of breast cancer", said Ian Johnson, nutrition researcher and emeritus fellow, Quadram Institute Bioscience, who wasn't involved in the research.
"When the group of sugary drinks was split into 100% fruit juices and other sugary drinks, the consumption of both beverage types was associated with a higher risk of overall cancer", reads the study conclusion.
"So this means if 1,000 similar participants increased their daily sugary drink intake by 100ml, we'd expect the number of cancer cases to rise from 22 to 26 per 1,000 people over a five-year period".
Susannah Brown, acting head of research interpretation at the World Cancer Research Fund, said the charity's own research had shown a link between obesity - which is associated with drinking too many sugary drinks - and cancer.
Touvier suggested that people should stick to public health guidelines that recommend limiting sugary drinks to a maximum of one glass a day. The findings may also taint the image of fruit juices, which are often perceived - and promoted - as healthy.
Responding to the study, the American Beverage Association stressed the safety of sugary drinks.
"More research is needed to understand if there is a direct link between sugary drinks and cancer", she added.