After an emergency meeting with his defence council on Thursday, the presidential palace announced that security would be stepped up in the wake of the "barbaric execution" of Gourdel. It also widened its vigilance alert for its citizens to cover 40 countries.
The move also comes days after Isis Islamic extremists called on Muslims to target the French and citizens of other countries that have joined the US-led coalition to fight the jihadist organization, branding the French “dirty” and “spiteful”.
On Thursday Interior Minister Bernard Cazeneuve said the beheading calls for a “strong response abroad and at home to protect our citizens.”
Following the meeting a statement from the Elysée said: "All France is in mourning after the barbaric execution of our compatriot Hervé Gourdel.
"This crime must not go unpunished. In these tragic circumstances, national unity is an imperative. As individuals and groups who seek to weaken us by dividing us, we must oppose them with the strength of our cohesion and a reaffirmation of our values.
There was no announcement however over a plan to up the warning level of France's national security alert system, known as “Vigipirate”.
The system, which has existed since the mid-90s when Paris was hit be terrorist attacks, is currently at level four out of five.
A police source told Le Parisien newspaper recently , there is no desire to up the threat level, “even though it could be justified” because it would increase the anxiety of the French people, “which is exactly what Isis is hoping to achieve”.
Paris also said Thursday it had widened its vigilance alert for nationals abroad from 31 to 40 countries including Asian nations, after a French hostage was beheaded in Algeria by jihadists linked to
the Islamic State group.
"We have extended the call (for vigilance) to some 10 more countries," Didier Le Bret, head of the foreign ministry's crisis centre, told AFP, adding Muslim countries in Asia were now included.
Hollande also pledged "determination, composure and vigilance" in the face of jihadi threats at an emergency cabinet meeting and announced that flags nationwide would be flown at half-mast for three days from Friday to mourn the loss of the 55-year-old mountaineer.
"Faced with this threat, we need national unity," he told the meeting, according to government spokesman Stephane Le Foll, who also announced France had carried out air strikes in restive Iraq on Thursday morning - the second in the space of a week.
France opposed the 2003 US-led invasion of Iraq but was one of the first to sign up for an active role in the campaign against the group that has rampaged through large areas of Iraq and Syria.
Paris has six Rafale fighter jets and just under 1,000 soldiers based in the United Arab Emirates, and on Friday carried out its first air strike on IS targets in Iraq, destroying a logistics depot.
Earlier Foreign Minister Laurent Fabius has said, "everything would be looked at again," including "what we want to do in Iraq and what will happen in Syria."
France has vowed to conduct aerial operations against Iraq in support of local forces fighting Isis but has stressed it will not deploy ground troops, nor will it expand operations to Syria, as the United States has done.
US, Saudi and Emirati warplanes bombed oil installations in eastern Syria overnight in a bid to cut off a significant source of funding for the Isis group.
However, Defence Minister Jean-Yves Le Drian seemed to open the door to possible action in neighbouring Syria, telling French radio on Thursday it was "a question that had to be asked."
Nevertheless, the minister stressed it was "an opportunity that is not on the table today. We have an important task to carry out in Iraq."