Isabelle Baldi, one of the scientists who led the French research, published in the British journal Occupational and Environmental Medicine, said: "Our study is part of that trend, but the results have to be confirmed."
Researchers examined 253 cases of glioma and 194 cases of meningioma reported in four French departments, or counties, between 2004 and 2006.
These patients were compared with 892 controls, or healthy individuals.
The comparison found a higher risk among those who used their phone intensively, especially those who used it for their work, such as in the sales industry. The duration of use in this category ranged from between two and 10 years, averaging at five years.
There were, however, unexplained anomalies. In contrast with previous research, the study found that cancer occurred on the opposite side of the brain to where the phone was habitually used, rather than on the same side.
"It is difficult to define a level of risk, if any, especially as mobile phone technology is constantly evolving," the study conceded.
"The rapid evolution of technology has led to a considerable increase in the use of mobile phones and a parallel decrease of [radiowave intensity] emitted by the phones.
"Studies taking account of these recent developments and allowing the observation of potential long-term effects will be needed."
In 2011, the International Agency for Research on Cancer warned that radiofrequency fields used by mobile phones were possibly carcinogenic.
The largest study to date on the risks of mobile phone use, the 2010 Interphone study, found no raised risk of brain tumours among those who regularly used mobiles.