Were there any movements to keep them together by Algerians, or was it prettymuch a universally agreed with movement? Did any have many supporters? What were their arguments?
Well the pieds-noirs (translated as "black feet", meaning European settlers living in Algeria) were both vociferous and violent in their attempts to keep Algeria as part of France. It's important to remember that, although European in ancestry, many of the pieds-noirs would be 2nd, 3rd or even 4th generation, and would have been born and raised in Algeria, spending their whole lives there. In their minds, this was their home as much as it was for any native Algerian.
There was a movement to essentially incorporate Algeria into France as an Arrondissement (or district), the slogan being "Tous Français, de Dunkerque à Tamanrasset", meaning "All French, from Dunkirk (in the extreme north of France) to Tamanrasset (in the extreme south of Algeria)."
The argument that the pieds-noirs often employed was that Algeria had benefited greatly from French involvement, through better educational standards, better infrastructure, a stronger economy, the introduction of democracy and well developed urban areas. However, they tended to ignore that these elements were normally only beneficial for pieds-noirs or white Europeans, and almost never for native Algerians who were normally treated as 2nd class citizens in their own country.
There were certainly a number of native Algerians who did believe in remaining as part of France as well, in particular the Harkis, native Algerians who fought with the French against the FLN. They are perhaps one of the most tragic stories of the war. Often veterans of the French army, they were abandoned when the French pulled out of Algeria, and subsequently massacred by the FLN and their supporters. Normally they were brutally tortured before being killed.
Is this the kind of overview you were looking for? If you want to read more about this subject, I highly recommend 'A Savage War of Peace' by Alistair Horne.