Δ$^{14}$CO$_2$ observations are increasingly used to constrain recently added fossil fuel CO$_2$ in the atmosphere. We use the LMDZ global atmospheric transport model to examine the pseudo‐Lagrangian framework commonly used to determine recently added fossil fuel CO$_2$ (CO$_{2ff}$). Our results confirm that Δ$^{14}$CO$_2$ spatial variability in the Northern Hemisphere troposphere is dominated by the effect of CO$_{2ff}$, whereas in the Southern Hemisphere, ocean CO$_2$ exchange is more important. The model indicates that the free troposphere, at 3–5 km altitude, is a good choice for “background,” relative to which the recently added fossil fuel CO$_2$ can be calculated, although spatial variability in free tropospheric Δ$^{14}$CO$_2$ contributes additional uncertainty to the CO$_{2ff}$ calculation. Comparison of model and observations suggests that care must be taken in using high‐altitude mountain sites as a proxy for free tropospheric air, since these sites may be occasionally influenced by (polluted) boundary layer air, especially in summer. Other sources of CO$_2$ which have Δ$^{14}C$ different than that of the atmosphere contribute a bias, which, over the Northern Hemisphere land, is mostly due to the terrestrial biosphere, whereas ocean CO2 exchange and nuclear industry and natural cosmogenic production of $^{14}$C contribute only weakly. The model indicates that neglecting this bias leads to a consistent underestimation of CO$_{2ff}$, typically between 0.2 and 0.5ppm of CO$_2$, with a maximum in summer. While our analysis focuses on fossil fuel CO$_2$, our conclusions, particularly the choice of background site, can also be applied to other trace gases emitted at the surface.