This is their first major operation in CAR since about 150 troops were deployed in recent weeks to Bangui, amid warnings of a genocide.
Around a quarter of CAR's 4.6 million population have fled their homes since conflict erupted in March 2013 between mainly Muslim and Christian militias.
The African Union and France have about 7,000 troops in the country.
They have been battling to curb the conflict, and the EU has pledged to send up to 1,000 troops and the United Nations (UN) about 12,000 troops.
French troops handed control of the airport in the capital, Bangui, to the EU force on Wednesday.
Bangui has seen some of the worst fighting, and AU troops escorted more than 1,200 Muslims out of the city on Sunday to protect them from the mainly Christian anti-balaka militia.
The EU force is under the command of a French officer, Maj-Gen Philippe Ponties, and is made up of French and Estonian troops.
Source: Index Mundi
Their deployment to the airport is intended to allow French troops to move elsewhere in the country.
UN officials and aid agencies have warned that hatred between Christians and Muslims could lead to a genocide and the partition of the country.
Few Muslims remain in Bangui, with most of them fleeing to the north or neighbouring states.
Christians form the majority in CAR, and the anti-balaka say they took up arms after coming under attack from the mainly Muslim Seleka rebels who seized power in March 2013.
Seleka leader Michel Djotodia was forced to step down in January, because of his failure to stem the violence.
He had been the CAR's first Muslim ruler. His supporters accuse troops loyal to the president he overthrew, Francois Bozize, of fuelling the conflict.

The furry explorer climbed inside the child's plaything and jammed its head through a small hole at the rear.
Despite its owners attempts to free it, the plastic proved too tough and the "unusual" emergency call-out was made.
Oxfordshire Fire and Rescue Service said the kitten was unharmed but its experience served as a warning against "diving into your presents too early".
Crews were called to a house in Stanford-in-the-Vale at about midday on Wednesday.
European Union (EU) troops have taken control of security at the Central African Republic's (CAR) main airport.
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A three-month old kitten had to be rescued by firefighters after it got stuck in a toy car.