Hydrochloric Acid is a strong Acid but Sodium Carbonate is a weak (?) base, so I would use an indicator that lies within the range of roughly 3 to 6 in pH, say methyl red, methyl orange or bromothymol blue, in order of increasing pH.
The longest inflexion is the one to consider. This occurs in the range of the methyl orange indicator. I suppose the acidity can be attributed to CO2 (an acidic oxide) as jetblack has pointed out.