I have quoted before from Calvin (via Myers) about “earthly things … which do not pertain to God or his Kingdom”, but do include “government, household management, all mechanical skills, and the liberal arts.”  Calvin continues by explaining how Natural Law enables man to run society:

Of [earthly things] the following ought to be said: since man is by nature a social animal, he tends through natural instinct to foster and preserve society. Consequently, we observe that there exist in all men’s minds universal impressions of a certain civic fair dealing and order. Hence no man is to be found who does not understand that every sort of human organization must be regulated by laws, and who does not comprehend the principles of those laws. Hence arises that unvarying consent of all nations and of individual mortals with regard to laws. For their seeds have, without teacher or lawgiver, been implanted in all men.

After extolling God’s common grace in giving man skills in other matters such as art, science, medicine, mathematics, etc. Calvin turns his consideration to the separate  category of man’s potential for knowledge of spiritual things.  In terms of “knowing how to frame our life according to the rule of his law,” Calvin considers separately the first and second tables: 

Surely [man's reason] does not at all comply with the principal points of the First Table; such as putting our faith in God, giving due praise for his excellence and righteousness, calling upon his name, and truly keeping the Sabbath [Ex. 20:3-17]. What soul, relying upon natural perception, ever had an inkling that the lawful worship of God consists in these and like matters? … Men have somewhat more understanding of the precepts of the Second Table [Ex. 20:12 ff.] because these are more closely concerned with the preservation of civil society among them.

Some notes: 

• “More closely concerned” is less than “completely definitive of.”  Calvin’s non-rigid connection between even just the second table and civil norms recalls a Klinean view of the Decalogue as being primarily and particularly a constitution for national Israel.
• “More closely concerned” implies, at a minimum, that the first table is “less closely concerned” with civil order.
• Calvin’s assertion that natural man cannot discern even an “inkling” of the particulars of the first table, seems to exclude the first table from Natural Law.
• That, combined with Calvin’s confidence in Natural Law’s ability to inform man’s regulation of society, implies that the civil sphere should have nought to do with the first table — so why did Calvin (though not a Theonomist) remain a Theocrat?