'State of war'
The EU force, around half of which will be French, is preparing to deploy near the eastern border with Sudan in coming weeks to protect refugees and aid workers.
The Chadian fighter group, the Union of Forces for Democracy and Development (UFDD), said in a statement that it now "considers itself to be in a state of war against the French army, or against any other foreign forces in the national territory".
Sarkozy said: "If we decided to send a European force to one side of the border and a mixed force on the other side it is because there are problems, conflicts, difficulties.
"If there were none we would not have decided to send soldiers."
UFDD fighters have been battling government forces loyal to Idriss Deby, the country's president, in eastern Chad since the weekend.
The fierce clashes have shattered a month-old peace accord between Deby's government and his main foes.
The fighters said French military aircraft had flown over their positions on reconnaissance missions for the government during heavy fighting on Thursday between the towns of Guereda and Adre, along the border with Sudan's Darfur region.
A statement from the UFDD said: "Providing diplomatic, strategic and logistical support to the tyrant Idriss Deby is an act of hostility and will be treated as such."
The UFDD has been fighting Deby in the east for two years.
While they have criticised France's support for him in the past, they have stopped short of direct hostilities with French forces.
Chad is a former French colony, and France is providing around half of the 3,700 EU peacekeepers who are due to start arriving early next year.
The EU force, which will also send soldiers to the northeast of the Central African Republic, is also intended to try to help contain a widening conflict in Sudan's Darfur region, which has pushed armed raiders and refugees across the border.
It will complement a bigger UN/African Union peacekeeping force planned for Darfur, where political and ethnic conflict triggered by a 2003 rebellion has killed at least 200,000 people.