In this paper, we apply two types of automatic balance mechanism (ABM) to the French first pillar pension system for private sector employees (CNAV). One is based on a tax gap ratio (TGR-ABM) and the other is the smooth ABM (S-ABM) developed by Gannon, Legros and Touzé (2013). Two long-run forecast scenarios over the period 2014-2063 are analysed. The first is optimistic (“benchmark”) and assumes a 4.5% unemployment rate and a 1.5% productivity growth rate in the long run. The second is more pessimistic (“prudent”), with a 7.5% unemployment rate and a 1% productivity growth rate in the long run. For the benchmark (respectively prudent) scenario, a TGR-ABM requires, now and for the next 50 years, a 2.8% (respectively 6.3%) decrease in pensions and a 2.9% (respectively 6.7%) increase in the tax rate. An S-ABM requires, for the benchmark (respectively prudent) scenario, an immediate 1.5% (respectively 3.6%) decrease in pensions and a 1.4% (respectively 3.5%) increase in the tax rate. In the long run (50 years), an S-ABM requires a 4.5% (respectively 9.1%) reduction in pensions and a 4.5% (respectively 9.1%) increase in the tax rate.