Under the watch of an increased police presence, it's business a usual at the Eiffel Tower, tourists from all over the world undeterred by threats of violence by Islamic State against France and French citizens.

But the French media take the opposite view, calling Islamic State the "New masters of terror" and reminding readers that allies of Islamic State hold one of their own, as a hostage.

French national Herve Gourvel was kidnapped in eastern Algeria on Sunday. The group holding him call themselves the Caliphate Soldiers and say if France does not stop its military assault on Islamic State, Gourvel will die.

But France says, while it's military won't join the fight in Syria, it will continue to bomb Islamic State targets in Iraq.

A hostage's life may be at stake, and Paris is on the defensive, but the French government says threats from Islamic State or its allies, cannot change France's position.