The couple and Fillon's former parliamentary colleague Marc Joulaud risk 10 years in jail and heavy fines.
The eagerly-awaited trial of the former presidential hopeful and his wife was due to start on Monday, but was delayed over a lawyers' strike.
Investigators say Fillon, 65, paid Welsh-born Penelope, 64, the salary of a parliamentary assistant between 1998 and 2013 -- up to 10,000 euros (almost $10,900) a month -- without her doing much, if any, actual work.
The trial kicked off with technical arguments as to whether some of the alleged crimes happened too long ago to be prosecuted under France's statute of limitations, and how to define the crime of misappropriating public funds.
The court must decide these issues before it can examine the merits of the case.
It could decide to refer the questions to an appeals court, in which case the trial would be postponed. If not, the defendants are expected to start presenting their case on Thursday.
The claims first emerged in January 2017, and torpedoed Fillon's shot at the presidency in elections that year.
Did she work?
They also contributed to the implosion of his rightwing Republicains party, pushing many voters toward the centrist party of now-President Emmanuel Macron.
Fillon has denied the allegations and insisted that Penelope -- charged with complicity -- did real work for him in his rural constituency of Sarthe.
But investigators say they have found little evidence of her efforts, and have seized on a 2016 newspaper interview in which Penelope declared: "Until now, I have never got involved in my husband's political life".
She had made a similar statement to Britain's Sunday Telegraph in 2007.
Joulaud, 52, stood in for Fillon in parliament when he was a cabinet minister and also hired Penelope as an assistant.
France's National Assembly has joined the case as a civil party, and said it could seek over a million euros (dollars) in compensation.