Jerome Cahuzac resigned in 2013 after it emerged he had once held an undeclared Swiss bank account and had lied about it to parliament.
If convicted, he faces up to seven years in prison and hefty fines.
The trial is seen as an embarrassment for Mr Hollande as he gears up for the 2017 presidential elections.
Mr Cahuzac struggled to make his way through hordes of journalists as he arrived at the court in Paris on Monday.
Before entering politics, Mr Cahuzac was a successful cosmetic surgeon who made a fortune providing hair implants for the rich and famous.
He was appointed budget minister by Mr Hollande in 2012 and gained a reputation as a vocal crusader against the use of overseas tax havens by the wealthy.
He initially denied a report by the investigative website Mediapart that he had kept an undeclared Swiss bank account until 2010.
But after a meeting with investigating magistrates in April 2013, he admitted having the account, which contained about 600,000 euros (Â£460,000). He said at the time that he was "consumed by remorse".
In the light of the scandal, President Hollande ordered his ministers to disclose their personal wealth.
Mr Cahuzac is charged with tax fraud and money laundering.
At the opening of the trial, Mr Cahuzac's lawyers challenged the constitutionality of the case against him, arguing that he has already settled his debts with tax officials and should not be tried twice for the same matter.
If the case is referred to the Constitutional Court the trial could be delayed.
Mr Cazuhac's ex-wife Patricia Menard is also on trial as a co-defendant along with financial advisers and a Swiss bank.
A former French budget minister, who was appointed by President Francois Hollande to tackle tax evasion, has gone on trial charged with tax fraud.