The C4 Pathway

Sugarcane is a $C_4$ plant (Hatch and Slack pathway).
In the mesophyll cells, $CO_2$ (as bicarbonate) combines with phosphoenolpyruvate (PEP), catalysed by PEP carboxylase, to form the 4-carbon oxaloacetic acid (OAA).
OAA is then reduced to malic acid, which carries the fixed carbon to the bundle sheath cells.
There malic acid is decarboxylated, and the released $CO_2$ is fixed again by RuBisCO in the Calvin cycle.
So the enzyme that first fixes $CO_2$ (into OAA and then malic acid) is phosphoenol pyruvic acid carboxylase.

In $C_4$ plants, the primary $CO_2$ fixation occurs in the mesophyll cells.
The enzyme PEP carboxylase (PEPcase) combines $CO_2$ with phosphoenolpyruvate (PEP) to form oxaloacetic acid, a 4-carbon compound.
PEPcase has a high affinity for $CO_2$ and does not react with $O_2$.
RuBisCO acts later, in the bundle sheath cells.
So the first $CO_2$ fixing enzyme in $C_4$ plants is PEP-carboxylase.