French officials have raised pressure this week to defend BNP Paribas bank from what they see as disproportionate penalties US authorities are set to impose.
Hollande says he will raise the issue at the dinner in a Paris restaurant, but in Brussels on Thursday Obama said he would not interfere in the judicial process.
French officials however have warned the threatened fine could have a dangerous impact on the economy and on bilateral relations.
They say that imposing a big penalty of 7.4 billion euros on the bank, one of the biggest in Europe, could destabilise the financial system, cut lending to businesses and so impede economic recovery.
Hollande, who has already written to Obama complaining about the size of the potential penalty, is to dine with him in Paris on the eve of ceremonies to mark the 70th anniversary of the D-Day landings that changed the course of World War II.
Hollande also hinted on Wednesday that talks to create the world's top trade deal between the EU and US were at stake.
"Nothing should jeopardise the partnership between France and the United States, because we are engaged in other discussions and we expect reciprocity," he said.
Accused of breaking US sanctions against Iran, Sudan and Cuba between 2002 and 2009, BNP Paribas also risks temporarily losing its US banking licence.
A number of other big European banks are at risk from US authorities for similar sanctions violations.
"This affair could serve as a trigger, for the countries whose big international banks are also susceptible to being caught up by the American procedures," French Finance Minister Michel Sapin told the Le Monde newspaper on Thursday.
French banks Credit Agricole and Societe Generale, Germany's Deutsche Bank and Italy's Unicredit are also being probed.
Many analysts say stiff penalties would neither bring down BNP Paribas nor create risks for the wider financial system.
But former European Central Bank chief Jean-Claude Trichet said penalising banks by prohibiting them from carrying out dollar clearing operations would create systemic risks.
"It is worse than disproportionate, it is a systemic risk for which there is absolutely no need in our country, Europe and the world," he said on BFM Business radio.
SHADOW OVER FREE-TRADE DEAL
French leverage would normally be limited against the US justice system, which jealously guards its independence.
But Sapin told the Le Monde newspaper: "This could affect the discussions underway on the free-trade treaty."
The proposed Transatlantic Trade and Investment Partnership could eventually establish the world's largest free trade and investment zone, covering some 820 million people and more than $1 trillion in annual two-way trade.
The EU and United States had hoped to wrap up discussions on the TTIP by the end of this year, although that deadline has been looking increasingly ambitious.
French Prime Minister Manuel Valls said "what we want is fair treatment for BNP Paribas, and this is the discussion that should take place tonight" between Hollande and Obama.
While respecting the independence of US prosecutors, Valls said the US authorities should also be "sensible" to the fact the issue touches upon France's economic independence.
US officials appear to be trying to calm the waters with Secretary of State John Kerry agreeing that the penalties should be appropriate.
"We obviously want whatever it is to be fair and to reflect an appropriateness to whatever it is that is alleged to have taken place," Kerry said Wednesday during a visit to Beirut.
Meanwhile The Wall Street Journal has reported that BNP's board is split over whether one or more heads should fall at the bank to assuage the US authorities, including that of chief executive Baudouin Prot, the report said, citing people close to the matter.
A source close to the talks between BNP Paribas and US authorities told AFP however that "the resignation of Baudouin Prot is not part of the negotiations".
Sapin also said on Thursday that a number of BNP Paribas employees had already been dismissed in connection with transactions that US authorities believe violated their sanctions.