Three parts do the work on most residential French doors.
Flush bolts or surface bolts on the fixed leaf. These are small sliding bolts set into the edge of the fixed leaf, one shooting up into the head of the frame and one shooting down into the sill or floor. When both are engaged, the fixed leaf behaves like a frame for the active leaf. When one is left open, or the keeper hole is blocked with dirt, the whole pair can be pushed in.
The lock on the active leaf. This may be a deadbolt and a latch set, a narrow mortise lock, or a multipoint lock with bolts along the edge. It locks into a strike fitted on the fixed leaf's edge, not into the wall.
The astragal. This is the strip that covers the gap where the two leaves meet. On exterior doors it keeps weather out and also covers the latch and bolt so they cannot be reached with a thin tool from outside.
A weak point in any one of these three parts weakens the whole opening.