how can common law jurisdictions enter into contracts with civil jurisdictions who do not have consideration?
It is important to remember that the assumptions in the answer below apply generally to common/law and civil jurisdictions but cannot be said to apply to them all. Another assumption made below is that all common law jurisdictions require consideration whereas civil law jurisdictions do not.
Common law citizens can typically contract with whomever they choose, due to the doctrine of freedom of contract. In essence there is nothing stopping a common law citizen from sending an offer to a civil law citizen in anticipation of it being accepted.
Any issues that arise with their contract, if there are any, will likely be due to the procedure in which the contract was formed not being adequate. Typically, clauses are placed in contracts to prevent these issues through terms that determine whether arbitration, or the laws of a particular jurisdiction apply to the contracts’ governance. Through knowing where any decisions concerning contractual issues are to take place, parties will know whether or not certain procedures are required to form their contract e.g. consideration.
If a consensus as to what law will be applied given a dispute has not been reached, there are numerous methods that can be adopted by the relevant states to determine what law will be applied, such as international agreements. The important thing to remember however is that a single set of governing laws will apply.
Simply, if the contract must abide by the governing law of a common law state, then consideration will be necessary for the contract. If a civil-law jurisdiction governs the dispute, the pre-contractual consideration will not be considered necessary.
Therefore, the answer to this question does not really concern how the parties contract, but whom determines the necessary provisions of said contracts enforceability.