Perhaps the most comprehensive work in the area of atmospheric CO2 levels over Phanerozoic time has been done by Berner (1990, 1992, 1993, 1997), who cites the work of most other people who have attempted to reconstruct atmospheric CO2 levels over the past 600 million years. For even earlier periods one can consult papers cited by Kasting (1993).
In very general terms, these long-term reconstructions of atmospheric CO2 levels depict a gradual rising back in time to approximately five times earth's current concentration at about 220 million years ago, followed by a dip back to near-current levels between 250 and 350 million years ago, with a rise to perhaps 20 times today's concentration between 450 and 550 million years ago. Beyond that point in time, the CO2 content of the air is generally portrayed as rising all the way to a full bar of presure (1,000,000 ppm) at 4.5 billion years ago.
ReferencesBerner, R.A. 1990. Atmospheric carbon dioxide levels over Phanerozoic time. Science 249: 1382-1386.
Berner, R.A. 1992. Paleo-CO2 and climate. Nature 358: 114.
Berner, R.A. 1993. Paleozoic atmospheric CO2: Importance of solar radiation and plant evolution. Science 261: 68-70.
Berner, R.A. 1997. The rise of plants and their effect on weathering and atmospheric CO2. Science 276: 544-546.
Kasting, J.F. 1993. Earth's early atmosphere. Science 259: 920-926.