Generation from synchronous machines in European power systems is decreasing as variable renewable energy penetration increases. Appropriate levels of system rotational inertia to ensure system stability, previously inherent in synchronous areas across Europe, can no longer be assumed. This work investigated the impact different levels of minimum inertia constraint have in Europe and in each synchronous area. Two scenarios with divergent decarbonisation ambitions were simulated for the year 2030 using a unit commitment and economic dispatch model. The key findings show that an increasing inertia constraint elevates total generation costs, variable renewable energy curtailment and carbon dioxide emissions across Europe for an ambitious decarbonisation scenario. When inertia constraints were applied to the contrasting scenario with a low decarbonisation ambition, decreases in carbon dioxide emissions of up to 49% were observed in some synchronous areas where the constraint was frequently active. The work also scrutinised the spread of inertia in the large synchronous area of Continental Europe. It emerged that some countries are likely to experience periods of low inertia even if an inertia constraint is applied at synchronous area level.