(Reuters) - Switzerland's largest bank UBS could face a fine of up to $6.3 billion if found guilty in a French investigation into whether it helped wealthy customers there avoid tax, a Swiss newspaper reported on Friday.

A French court has already ordered UBS to deposit a 1.1 billion-euro ($1.4 billion) guarantee to cover a portion of potential fines in the case, but Swiss newspaper Le Temps said it had seen a legal document showing the bank could face a penalty of up to 5 billion euros. 

The document, written by two judges, is dated July 23, the same day the bank was first ordered by French officials to pay the guarantee.

Le Temps quoted the document as saying "the business model of UBS Switzerland was to offer its clients bank secrecy in contradiction to (French) fiscal authorities".

An official for UBS was not immediately available for comment. 

The bank issued a strongly worded condemnation of the 1.1 billion euro demand when it was issued in July. Last month, the bank said it would again appeal against a French court ruling demanding the payment after an initial appeal was turned down. 

Shares in UBS were down 1.9 percent at 0829 GMT, lagging the European banking sector which was up 0.8 percent. 

On top of the French case, UBS is also dealing with allegations it was involved in rigging foreign exchange rates. The bank warned earlier this week it faced new fines after confirming it was holding talks to settle these allegations. 

(1 US dollar = 0.9558 Swiss franc)

(1 US dollar = 0.7908 euro)

(Reporting by Joshua Franklin; Editing by Mark Potter)