The Swedish TV4 is not the best source to get information from. Every information channel has their habits and sources.
Sweden does not support with aircraft, but they support in other ways.
France asked after a large part from Swedish smart weapon stocks, which Sweden, or the government of Sweden promised to send. Sweden are also involved in other operations with IS (Iraq+), with support of Special Forces, as they do in central Africa. They also discussed ways to help France with more military support in Africa to release French troops for IS operations.
Sweden are also one of few countries in Europe taking hundreds of thousands refugees from Asia and Africa, with try to help at first people from Syria who is outbombed by Assad and Russia air bombing and refugees from environment uncontrol (ex Ethiopia). A huge cost, even to administrate the help to frustrated people outbombed from their own countries. The costs for the refugees is higher than the countries spend of military actions against IS. Sweden is one of few EU members who help refugees from other countries (as Germany, Austria). But the majority in the parlament was for to send France more help, but they choose to not take the match now. A majority of Sweden is for an association with NATO, and were is forces involved for it in the future. They are hindered by extrem right thinking. Today were are a very lot of contacts and military gaming with NATO planners, as military exercises for force cooperation.
It is still open to send airplanes.
I am sure Sweden is one of the first of many to build up a new Syria or work for the upbuilding of a new Syria and help to the refugees in their camps now. A huge cost. Their Syrian infrastructure are today destroyed.