Michele Alliot-Marie, the French interior minister, said the explosives were "relatively old" and had been hidden in the cistern of one of the lavatories.
"The explosives had not been primed which indicates there was no risk of explosion," she said outside the store on Boulevard Haussmann.
The warning, sent by letter to AFP, a French news agency, said the explosives were in the men's toilets on the third floor of the Printemps store in the city centre.
The letter read: "If you do not send someone to intervene before Wednesday December 17, they will explode.
"Send the message to your president that he must withdraw his troops from our country before the end of February 2009 or else we will take action in your capitalist department stores and, this time, without warning."
Estelle Youssouffa, Al Jazeera's correspondent in Paris, said: "French authorities... are extremely cautious about the claim by this group called the Afghan Revolutionary Front. It is completely unknown.
"They say they are examining the letter sent to the AFP news agency this morning. That letter was extremely precise as it explained where the five explosive charges were placed in the department store and that's exactly where the police discovered them.
"There were no detonators so they could not have exploded. The sign is very clear. It is a warning for France to withdraw its troops from Afghanistan."
'No Taliban tactic'
Zeina Khodr, Al Jazeera's correspondent in Kabul, Afghanistan said: "No-one has heard of this group ... not even the Taliban.
The fact the group was calling for the withdrawal of foreign forces from Afghanistan shows they share the same goal as the Taliban.
However, many here believe the incident in France was not a Taliban tactic - they would not have left explosives without a detonator.
"An Afghan MP told us that one cannot rule out the fact the group in France may have something to do with internal French politics - we know there are some groups in Paris who are against the presence of French troops in Afghanistan."
The area where Printemps is located is crowded with large department stores which are normally packed with Christmas shoppers at this time of year.
France has some 2,600 troops stationed in Afghanistan and has received threats of attacks in mainland France unless it removes the soldiers.
In a separate development, police in Paris arrested seven people on Tuesday suspected of having links to groups that send fighters to Iraq, the French AFP news agency has reported.
French intelligence officers and anti-terrorist police first arrested a young Frenchman who had converted to Islam and then detained six people he associated with, police officials said.
The police said the arrests were not connected to the Paris department store incident.