It'll be different...
When CO2 dissolves in human blood, it becomes carbonic acid. The carbonic acid releases H+, acidifying the blood a little (but a very clinically relevant amount), and most of the CO2 circulates as bicarbonate ion (HCO3-). Acidifying any bicarbonate solution is famously fizzy as the CO2 is released in the reverse reaction.
Some (10%) of CO2 does move through human blood as dissolved gas. But it's nonpolar, and adding HCl to blood should if anything make the aqueous solution even more polar, so I would hazard a guess you'll have even less than 10% solubility of gas.
Logan Kearsley pointed out that adding HCl across one of the carbon dioxide bonds gets you chloroformic acid, but I think the equilibrium concentration of this compound is low, and it will have little effect on bulk CO2 transport. Similarly, it is possible to protonate CO2, but low stability means it should only be a curiosity unless some advanced biochemical means is evolved to change that.
Now in human blood some of the CO2 travels attached to hemoglobin (carboxyhemoglobin), but I think we're well into the range of acid hydrolysis of proteins, so let's scratch that one also.
What that leaves us is inorganic acid-stable catalysts which have evolved to sort of take over from proteins. The PROTOTYPE of these might be aluminum oxide, which adsorbs CO2 on its surface. But we're talking about a living being, which can presumably work wonders with its internal alumina. Even in inorganic industrial applications, alumina has many possible structures and catalytic activities, and your organisms will be assembling it atom by atom in a controlled way. So I'm going to go with alumina moving the CO2 at high efficiency in a manner fairly analogous to how hemoglobin carries oxygen.