Militarily, they could have maintained control over the entire country of Algeria indefinitely. Troops and aircraft from metropolitan France, supported by the non-Arab/Berber population would have been enough to maintain control of the larger towns and keep the roads/ports open. There were also around100,000 Muslims bearing arms in support of the French regime, a figure that was probably comparable to the number of FLN members actually engaged in violence.
The real challenge for keeping France in Algeria was political. The Fourth Republic's governments did not last long, and the seemingly intractable conflict in Algeria excacerbated conflicts between the political parties, and well as between the military and the government. Many soldiers, especially those on the ground suspected that leftists in Paris were either defeatists, or seeking to maneuver them into a military defeat such as had taken place in Vietnam. The parties of the Left in turn saw the conflict as immoral, and many were openly sympathetic to the aims of the FLN.
It was, of course, a military coup designed to thwart negotiations with the FLN that brought De Gaulle to power. I don't think that preventing the coup and letting the Fourth Republic muddle along would change the dynamics of the conflict very much. But without De Gaulle, a fragile Fourth Republic government would have a harder time committing to peace, especially when it was apparent that there would be no real place for the million or so Europeans living in Algeria under any non-French government.