A

Step 1: Identify the configuration of capacitors. The capacitors $C_1$ and $C_2$ are in parallel between the two batteries with electromotive forces (emf) $\varepsilon_1$ and $\varepsilon_2$.
Step 2: For capacitors in parallel, the potential difference across each capacitor is the same and equal to the potential difference of the respective sources. Hence,
The potential difference across $C_1$ is:
$$ V_{C_1} = \varepsilon_1 $$
The potential difference across $C_2$ is:
$$ V_{C_2} = \varepsilon_2 $$
Step 3: Conclusion: The potential difference between the left and right plates of capacitor $C_1$ is $\varepsilon_1$ and for capacitor $C_2$ is $\varepsilon_2$. Thus, the correct answer is option A.