Interior minister Gérard Collomb says all the militants back from war zones in Iraq and Syria are subject to investigation by public prosecutors.
Man, who had photographs of and interviews with Kurdish militia fighters on him, has appeared in court on suspicion of aiding a terrorist group.
Hollande spoke as he met French soldiers in Iraq who are part of a US-led 60-member coalition carrying out air strikes against Islamic State.
In last New Year message of presidency, Hollande also paid tribute to those killed in terror attacks this year, including the 86 who died in Nice.
Report says Rafale fighter planes took off from the Charles de Gaulle carrier to take part in an attack on Islamic State's Iraq stronghold Mosul.
Figures show little let-up in numbers joining Islamic State despite bombing of IS strongholds and crackdown by authorities within France.
The claim made in jihadist group's magazine Dabiq raised speculation the two men may have been suicide bombers who targeted Stade de France.
Two raids against IS targets in Syria and Iraq were launched from the Charles de Gaulle which arrived in the eastern Mediterranean on Monday.
Attacks come as US defence secretary urges European allies to join forces to defeat IS and French police raid 128 addresses overnight.
While massive numbers of refugees continue to arrive in Europe, there is a perception among many in France that the country is something of a ‘promised land’ for asylum seekers, a dream destination about to be overwhelmed by the influx. But in reality, the self-proclaimed “land of human rights” figures way down the wish-list of those currently seeking to settle in Europe, even among francophone refugees. In this analysis of the crisis, which on Sunday saw Germany closing its southern borders, Mediapart's specialist writer on migratory issues, Carine Fouteau, examines why the majority of refugees are now spurning France.
The families were the first of up to 1,000 refugees from Syria and Iraq expected to be given asylum in France this week.
A group has claimed that attacks near the city of Haditha in the west of Iraq were carried out by two Frenchmen.
Voluntary centre will aim to reintegrate young French citizens who return from conflict zones such as Syria but who do not face prosecution.
The French Parliament this week formally adopted a new anti-terrorism law, part of which aims to stop terrorists using the internet to attract recruits and plot attacks. It will allow the authorities to block websites that “condone terrorism” and will create a new offence of “individual terrorist enterprise”. One key objective is to stop the “preparation” of attacks via the web. The government, which has rushed these measures through, says they are needed to combat the growing use of the internet and social media by terror groups and in particular to tackle the threat of so-called “lone wolf” terrorists operating in France and elsewhere. But civil liberties groups, judges and the state body that oversees the impact of digital technology have condemned the law as an attack on freedom, ineffective and unworkable. Jérôme Hourdeaux details the new measures.
The French defence ministry said two Rafale jets destroyed Islamic State pick-up trucks in the Tikrit region during a reconnaissance mission.