These two weak acids have similar disassociation constants in water. A low Ka indicates a relatively small number of acid molecules will form an anion stabilized by water. Two weak acids with similar disassociation constants will coexist in a solution without interacting. If two weak acids have very different Ka then there can be a reaction. In this case nothing would happen. For more generalized information search for mixture of weak acids.
Carbonic Acid
$$\ce{H2CO3 + H2O <=> HCO3- + H3O+}$$ $$K_a = 4.3 \times 10^{-7} = \frac{[\ce{H3O+}][\ce{HCO3^-}]}{[\ce{H2CO3}]}$$
Citric Acid
$$\ce{H3C6H5O7 + H2O <=> H2C6H5O7- + H3O+}$$ $$K_a = 1.8 \times 10^{-6} = \frac{[\ce{H3O+}][\ce{H2C6H5O7^-}]}{[\ce{H3C6H5O7}]}$$
