Speaking in Paris after talks with UK PM David Cameron, Mr Hollande confirmed French aircraft carrier Charles de Gaulle would join the military action.
It comes as the Belgian capital, Brussels, remains on the highest level of terror alert for a third day.
Suspected Paris attacks gunman Salah Abdeslam remains at large.
The two leaders agreed to step up co-operation on countering international terrorism, including increased data-sharing and sharing of airline records.
The Islamic State group has said it was responsible for the Paris attacks, in which 130 people were killed.
“I firmly support the decisive action taken by President Hollande to strike Isil [IS] in Syria, it is my firm belief that we should do so too,” Mr Cameron said in a statement at a news conference.
Mr Hollande said: “We will intensify our strikes, choosing targets that will do the most damage possible to this army of terrorists.”
In Brussels, the federal prosecutor’s spokesman said five people had been arrested following a police operation on Sunday night in the Brussels region and in the Liege region.
These arrests bring to 21 the number of people arrested as part of Belgium’s ongoing terror alert.
Earlier, Mr Hollande and Mr Cameron visited the Bataclan concert hall, where at least 89 people were killed.
Mr Hollande will be meeting the US and Russian presidents later this week.
Mr Cameron said he had offered the French air force the use of the RAF Akrotiri base on Cyprus to mount strikes on IS as well as RAF air-to-air refuelling support.
In the Brussels region, universities, schools, large stores, shopping centres and the metro system will stay closed on Monday, following renewed warnings of possible attacks. Soldiers are patrolling the streets of the capital.
Belgian Prime Minister Charles Michel said that everything was being done to return the city to normal as quickly as possible – but the authorities feared a repeat of the events in Paris.
Brussels has been on lockdown all weekend amid a manhunt for Salah Abdeslam, who is suspected of being among the assailants who killed 130 people in Paris 10 days ago.
Mr Michel told reporters that authorities feared “an attack similar to the one in Paris, with several individuals who could also possibly launch several attacks at the same time in multiple locations”.
The Belgian authorities have so far charged three people with involvement in the Paris attacks.
French media have reported that nine militants carried out the attacks on 13 November, and seven died.