At a joint news conference, Obama said the United States and France have made progress in "four key areas," including Iran sanctions.
"President Hollande and I agree on the need to continue enforcing existing sanctions," Obama said, "even as we believe that new sanctions during these negotiations would endanger the possibility of a diplomatic solution. And we remain absolutely united on our ultimate goal, which is preventing Iran from obtaining a nuclear weapon."
Obama said a "credible threat of force" led to a plan to destroy Syria's chemical weapons.
The two countries are also "major trading partners," Obama said, adding, "President Hollande's visit to Silicon Valley this week underscores our commitment to new collaborations in science and technology."
Obama cited progress in a third area -- "expanding the cooperation and clean-energy partnerships that make our countries leaders in the fight against climate change." The U.S. president said in a fourth area: "We're moving forward together on key global development initiatives: Food security and nutrition that can lift 50 million Africans out of poverty; our determination to replenish the Global Fund to fight AIDS, TB, and malaria -- and I'm pleased that we're joining with partners around the world on a new global health security effort to combat infectious diseases and save lives."
Hollande spoke of past meetings with Obama, and cited French peace efforts in Africa.
Hollande made the first visit to the United States by a French head of state in almost 20 years, which included a formal state dinner at the White House.
In earlier comments to reporters Tuesday, Hollande said it was united American and French resolve in the face of chemical weapons attacks by Syrian President Bashar Assad against civilians that led to a diplomatic solution and the eventual agreement Assad would hand over his stockpile. He added peace talks between the two sides in Switzerland are a good first step to finding a political solution to the nearly 3-year-old civil war.
"Geneva is a possible step in the right direction, but we will have to make headway, we will have to cooperate more, make sure our [diplomatic] services cooperate more," Hollande said. "We need to support the opposition. We need to make sure that the choice is not between dictatorship on the one hand and chaos on the other."
Obama said he's accepted an invitation from Hollande to visit France in June to commemorate the 70th anniversary of the allied D-Day invasion that liberated France in World War II.
"It's no exaggeration that we stand here because of each other," Obama added. "We owe our freedom to each other."
In return, Hollande expressed thanks to U.S. soldiers "who left their homes to liberate my country and Europe."
He also spoke of the current U.S.-French alliance to improve global prosperity and combat both terrorism and climate change.
After a one-on-one in the Oval Office, the leaders moved to the Cabinet Room, where the meeting expanded to include Vice President Joe Biden and the official U.S. and French delegations, the White House said.
The dinner, only the seventh hosted by the Obamas, took place in a heated tent on the White House lawn, USA Today reported. The guest list included Bradley Cooper, an actor famous for speaking French, New York Times editor Jill Abramson, Stephen Colbert of "The Colbert Report" and singer Mary J. Blige.
In their exchange of toasts, Obama noted France played a role in ending slavery in the United States.
"One young American lawyer went to Paris and was deeply moved to see white and black students studying together," Obama said. "And that young American was Charles Sumner, who -- inspired by what he saw in France -- became one of our greatest abolitionists, helped to end slavery, and is one of the reasons that all of us can be here this evening as full citizens, free and equal."
The Obamas offered Hollande a strictly American menu with rib-eye beef and oysters as the main course, washed down with California and Washington state wines.
"When you look at the agenda between the United States and France today as against 10 years ago, we have made significant progress both in terms of our bilateral cooperation but also how we work together to deal with issues around the world," a senior administration official told reporters Monday.
"Let's just say that we've come a long way from 'freedom fries' and are now working together on multiple continents to promote peace and security and economic growth and development," the official said.
"Freedom fries" was a political euphemism for french fries coined in 2003 by Rep. Bob Ney, R-Ohio, who as chairman of the committee with authority over House cafeterias ordered "French fries" be renamed "freedom fries" on House food-service menus to indicate displeasure with France's lack of support for the 2003 U.S.-led invasion of Iraq.
Working with Rep. Walter B. Jones Jr., R-N.C., he also changed French toast on the menu to "freedom toast."
Ney told reporters his action was "a small but symbolic effort to show the strong displeasure of many on Capitol Hill with the actions of our so-called ally France."
France is widely considered the oldest U.S. ally because it fought alongside the colonies in the American Revolutionary War.
The "freedom" names were quietly changed back in July 2006, after Ney left the committee.