Why is a civil legal system referred to as a system of “civil” law? In what sense is it “civil”? Does the name derive from origins in or association with the civil code or code civil? In this case, what was “civil” about the civil code? Was it distinct from a separate criminal code?
One part of the question wasn't very squarely answered by the other two very solid answers.
what was “civil” about the civil code? Was it distinct from a separate criminal code?
The civil code was distinct from a separate criminal code.
The civil code covers "private law" which is the law regarding the rights of citizens vis-a-vis each other.
The criminal code covers actions of people which the state may intervene of its own accord and in its own right to criminally punish.
The Napoleonic Code in early 19th century France, which was the first modern civil code and was patterned after the 6th century Corpus Juris Civilis in the eastern Roman Empire, was part of a package of French revolutionary reforms which also mandated that all crimes be codified.
The goal in both cases was to protect the average person from being abused by secret laws known only to elites that could be used against them.
Civil law countries are countries which have at their core a civil code comparable to the original French Civil Code (which remains on the books with only minor modifications from its original version in the very early 1800s).
Common Law Systems Compared And Other Senses Of The Term "Civil"
In contrast, in "common law" countries, whose legal systems are all derived from the English legal system, the body of private law set forth in the civil codes of civil law countries are instead mostly embodied in a tradition of case law precedents. Those case law precedents are ultimately traceable back to English case law precedents and to its system in which judges make law through the process of decided cases that serve as common law legal precedents. The body of law made in England and its successors through these case law precedents is called the "common law", with the commonality referring to the fact that these precedents were originally common to and binding upon all English people subject to the authority of the British monarch.
Confusingly, in common law countries, the term "civil" also refers to the non-criminal law aspects of the law, sometimes including not just "private law" but also non-criminal parts of the "public law" which governs the relationship between the individual and the state, or between and among state entities.
Also confusingly, in common law countries, some jurisdictions still have, and many jurisdictions once had, non-codified criminal offenses defined in case law formed by the same method of accumulated precedents traceable back to English precedents. These non-codified crimes are called "common law crimes".
The term "common law crime" is also used to refer to codified crimes that were also crimes at common law, in contrast to crimes that exist solely as a result of statutes and are often regulatory in nature (e.g. criminal traffic offenses).
Civil comes ultimately from civis, meaning citizen, but its roots lie in (reconstructed) proto-Italic *keiwis, meaning "society," coming from the Indo-European *ḱey, meaning "to settle." The obvious semantic connection is through the concept of a settlement, a village or town (indeed, by Latin times, civitas, "city").
Civil codes themselves are concerned with the orderly operation of society, defining and governing relationships that people have with each other and with the state. It is therefore not difficult to see how this relates to both senses for which the civ- root has been used, denoting both social constructs that bind people together as well as the people so bound.
The people who came up with the name "code civil" did not likely have all of this etymological history in mind; but I would add to Dale M's correct assertion "civil means of the citizen" that it also means of society.
Civil means "of the citizen"
In both French and English and, originally, Latin.
So, "civil code" is the law of the people - more or less.
It's original use in describing law was in the 6th century Corpus Juris Civilis ("Body of Civil Law") in Byzantium (the Eastern Roman Empire).
A collection of fundamental works in jurisprudence, issued from 529 to 534 by order of Justinian I, Byzantine Emperor. It is also sometimes referred to metonymically after one of its parts, the Code of Justinian.
The Latin root word gives us many English words: citizen, city, civic, civilian, civilisation, and, of course, the word civil with its multitude of definitions, including its three legal meanings:
a : of, relating to, or based on civil law
b : relating to private rights and to remedies sought by action or suit distinct from criminal proceedings
c : established by law