Drinking soda doesn’t just threaten to make us fat, it could be linked to a higher risk of cancer, judging from a new study. But here’s the more surprising part: so could fruit juices.

Increased daily consumption of about 3.4 ounces of soda — roughly a third of a can of Coke — was associated with an 18 percent greater risk of some cancers in a study published in the British Medical Journal. The likelihood of breast tumors alone rose even more, by 22 percent. When people drank the same amount of unsweetened fruit juice, they were also more likely to develop cancer, the researchers found.

The research, part of a broader effort carried out in France to investigate links between nutrition and health, is one of the first to find a connection between sweet drinks and cancer. The findings may also taint the image of fruit juices, which are often perceived — and promoted — as healthy.

“All beverages — either with sugar or without — are safe to consume as part of a balanced diet,” the American Beverage Association said in a statement. Beverage companies are working to provide more choices with reduced or no sugar, smaller package sizes and clear calorie information, according to the industry group.

The researchers tracked 97 beverages and 12 artificially sweetened ones, including carbonated ones, sports drinks, syrups and pure fruit juices. The correlations they found don’t necessarily mean the beverages alone lead to cancer. The study didn’t seek to understand the reason for the link, though the researchers speculated that sugar’s effect on visceral fat, blood-sugar levels and inflammation may play a role. Additives found in sodas and pesticides in fruit could also have an impact, they wrote.

“These data support the relevance of existing nutritional recommendations to limit sugary drink consumption, including 100 percent fruit juice, as well as policy actions, such as taxation and marketing restrictions targeting sugary drinks,” the authors wrote in conclusion.

Taxing on sweet products and labeling the front of packages can help reduce sugar consumption, especially if pure fruit juice is included in the measures, according to a study from the University of Waterloo published in May.

The French study found no increased cancer risk from sugar-free drinks, although so few of the people studied consumed them that the results may not be significant, the researchers said. Water, unsweetened tea and coffee also showed no heightened risk.

The research is part of France’s NutriNet-Sante, a web-based study following about 100,000 volunteers since 2009.