Hollande, who came to power in May 2012, is expected to announce new measures to boost the French economy, including lower charges for companies, cuts in public spending and a simplification of business regulation.
Threat to sue
Hollande and Trierweiler are scheduled to make a state visit to the United States in February and are set to attend a state dinner with President Barack Obama and his wife Michelle on Feb. 11.
On Friday, Hollande, 59, threatened to sue celebrity magazine Closer, complaining of breach of privacy after it said he was having an affair with Gayet, 41.
Closer published a series of photos of a woman resembling Gayet entering a Paris flat close to the Elysee presidential palace, followed by a man masked by a black motorcycle helmet who the magazine said was Hollande.
Gayet, a mother of two, has dozens of film credits to her name but is little known outside France. Last year, she starred in "Quai d'Orsay", in which she plays a vampish diplomatic adviser in the foreign ministry.
In March last year she filed a complaint with the Paris prosecutor for breach of privacy over Internet rumours alleging she had a relationship with Hollande.
(Read more: France'sHollande has tight window to step up reform)
Hollande and Trierweiler, a journalist for celebrity magazine Paris Match, are not married but have been in a long-term relationship for several years.
"Turn the page"
Hollande has four children from a previous relationship with Segolene Royal, a senior member of his Socialist Party who ran for president against Nicolas Sarkozy in 2007. Royal announced their separation right after she lost the election.
Speaking on France 2 televison on Sunday, Royal declined to comment on the affair, saying that French people had more important things to worry about.
"It is necessary to turn the page and get back to work," she said.
Opposition leader Francois Coppe, head of the conservative UMP party, said the affair was "disastrous for the image of France abroad".
At home, the reports of Hollande's affair have had little effect on his image and French media at the weekend mainly focused on Closer's unprecedented breach of presidential privacy rather than on the alleged relationship with Gayet.
A poll by Ifop showed that 84 percent of the public had not changed their opinion about Hollande following news of the affair and that 77 percent considered it "a private affair that only concerns Francois Hollande".
"At the moment, the revelations about his liaison with Julie Gayet have no effect on public opinion. In fact, he is already so unpopular that there is no change," said Ifop analyst Frederic Dabi.
In November one survey gave Hollande an approval rating of only 15 percent. He is the most unpopular president in France's modern history according to several polls.
Hollande's Culture Minister Aurelie Filippetti said the French were responsible and mature and the Ifop poll showed they respected one another.