It seems there are two distinct questions now being asked or implied:
What relevance does a civil declaration of nullity have in the Catholic Church?
How does the Church determine the validity of the marriages of two non-Catholics?
As noted already, a civil declaration of nullity does not necessarily have any weight. Such a decision could be used as evidence in an ecclesiastical process but the Church must examine that marriage as it would any other. In the end, both Church and State might come to the same conclusion and say the marriage was invalid/null from the beginning. But, the two decisions/processes are separate.
The second question (actually, both questions) can begin to be answered by
Dignitas connubii, art. 4, which can be found here:
vatican.va/roman_curia/pontifical_councils/intrptxt/documents/rc_pc_intrptxt_doc_20050125_dignitas-connubii_en.html
In summary, that article states that the secular law which binds a person is considered by the ecclesiastical Judge and, as long as it does not contradict divine law, it is used in judging the validity of the marriage.
I would also point out that the law of the Church sees a difference between a “marriage” that was *never *recognized by the State and one that was recognized but then declared null (to keep it simple, let’s say that both Parties are unbaptized). The former would be equivalent to that of a Catholic who “married” with no regard for canonical form. The latter would be like any other marriage that enjoys the presumption of validity.
Dan