I don't know the area around Bayonne, but in general you'll find that the "international sections" in the public schools are usually for older students - usually college (i.e. junior high school) and lycée (high school). To find an international school for younger children, you're pretty much limited to the private schools - which aren't necessarily available everywhere in France.
At the ages your children are, they'll pick up the French language like little sponges, though. You may want to consider enrolling them in the public schools.