Further tests are now being carried out to see if the tourists are infected with the faster-spreading mutation of the virus believed to have originated in England, which has caused concern across Europe.
The regional ARS health authority told AFP that all 26 members of the group had undergone tests and 14 were so far positive, with other results still to come in.
The group, which according to French media are British students, have been in quarantine in their accommodation in the resort of Vallorcine, near the French Alpine hub of Chamonix, with police making sure their isolation is being respected.
No one has been hospitalised so far and the self-isolation rules are being respected, the local prefecture added. A substantial effort of contract-tracing is also underway to prevent the spread of the cluster.
Regional health authorities are also investigating whether the group travelled directly from the UK to the resort or not. According to France Bleu some of them had taken a TGV high speed train between Lille and Lyon before arriving in Haute-Savoie.
So far just one to two percent of coronavirus cases in France are believed to have been caused by the fast-spreading variant, but officials fear it could drastically worsen the health situation.
A new lockdown “would probably become an absolute necessity” if the spread of this variant increased “significantly” in France, Health Minister Olivier Véran warned on Thursday.
The purpose of the group's visit or their arrival date was not immediately clear.
Alpine skiing is almost impossible in France at the moment as ski lifts are shut to prevent the spread of the virus. But hotels are open and other winter activities such as snow-shoeing and cross-country skiing are still allowed.