It is possible. It is also likely to be a very different France by now than the France we are used to. In 1960, France's population was 46 million and Algeria's population was 11 million. If Algeria was fully part of Metropolitan France, the combined population would be 57 million of which about 25% of France would be Muslim.
By 2013, if nothing changed, Metropolitan France would have a population of 65 million (3 million Muslims) and Algeria a population of 37 million. A grand total of almost 100 million people of which only 3/5 are European Christian. And by then, immigration back and forth will have progressed so much that separation would be almost impossible. French identity would be inextricably linked with Islam even without a Muslim majority. And the combined nation would be the single largest nation in Europe with probably a great deal of France's industry located on the Algerian Coast since Algeria has major coal deposits on the coast and major iron, copper and uranium deposits in the Hoaggar Mountains as well as oil. Whether the EU would be together under the circumstances is unclear. Nor is it clear if Tunisia would be independent or whether it would have been absorbed into Algeria-France. Morocco woud likely be indepandent. Libya might still be part of Italy.And the border of French West African colonies that became independent might have been drawn further south too, with possibly Mauretania and northern Mali and Niger becoming part of Algeria-France because of it's low population, prospect of resources and need to build infrastructure across the Sahara to access the rest of the African nations.