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So I am a 3L at a Louisiana law school where I've been instructed in civil law (i.e. civil law property & civil law contracts).

I am planning to take the bar exam out of state. I know the MBE requires common law property & contracts.

Is it reasonable to expect that I could pass the bar exam having never taken common law property & contracts??? Can I learn these for the first time this summer while at the same time studying for the Bar Exam generally??

Any advice is appreciated!

Yes. Your bar prep course will be all that you need for those subjects, and every other subject on the test. Don't worry about the bar until after graduation. Good luck.

Since you haven't been exposed to the common law stuff, I would start your bar prep the week after graduation. No point in delaying if you need to learn a couple of pretty big subject areas.