Yes it was. We find early attestation in 6th century Burgundy, giving formal recognition to the concept under King Gundebald. It was one of several "Ordeals" that one could go through in lieu of trial to prove innocence, the thinking being of course that one in the right would win with God's guidance (I'm not a medievalist, so the general concept of trial by ordeal is something another person would need to expand on, as I approach trial by combat as the antecedent to the later duel of honor). Obviously there was a great defect here to more modern eyes, since the winner often was the better fighter, but this was a criticism even then. Incidents where the weaker man clearly won, for this reason, were especially noted. One famous example in the 9th century was between Gontran, a cousin of the Count of Gastonois and a young man named Ingelger. The Count had died, and Gontran accused the man's wife of the murder. Ingelger pleaded to be allowed to stand as the lady's champion (he was her godson), and triumphed in the fight, beheading his felled adversary, and being presented with a great deal of land by the Countess.
Although in the early Middle Ages, there was at least some support from the Church, it quickly soured, and we see a number of laws and edicts that sought to limit or stamp it out, and in 1215, priests were prohibited from being involved in any way, making the trial by combat an essentially secular proceeding. It survived for several more centuries however, but slowly began to die off as an explicit replacement for trial. One of the last true judicial duels was that between Jean de Carogne and Jacques le Gris, the latter having been accused by the former's wife of rape. Carogne would defeat the accused - favorite of the King - in combat before the court and many notable dignitaries. Fought in 1387, this was the last judicial duel in France to be sanctioned by the Parliament of Paris, and the controversy and distaste that it brought for many no doubt played a part in the demise there. Several more would occur over the next century or so in the distant parts of France, but further requests were denied by Parliament, losing the institution much of its standing.
Fought around 1400, one of those unsanctioned trials is perhaps is one of the most interesting trials by combat to ever occur, being between a man and a dog. Aubry de Montdidier was murdered with no witnesses except his dog, who stayed by the body for several days until the poor greyhound was too hungry, so set off to find food. A friend of his master found the dog, who then led him to his poor master's body. Some time later, upon seeing the Chevalier Maquer, who was known to have no love for Montdidier, the dog became vicious and had to be restrained. This was taken as an accusation, and trial by combat arranged between the alleged murder and his canine accuser. Just how the duel proceded is unclear as several, varied accounts exist regarding this episode, either Maquer was buried waist deep with shield and stick, or else he was given a lance, but regardless, he couldn't fed off the dog, which set upon him with such viciousness that he soon begged for mercy and confessed, following which he was hanged.
As I said though, the explicit replacement of trial with the adjudication of a criminal proceeding by feat of arms was fast dying out by the late 14th century, even if it would continue for some time. There is a shifting which is seen in the late medieval/early modern period from there to the duel of honor, which is well illustrated by the 1547 duel between the Baron of Jarnac, a minor lord with low standing, and La Châtaigneraye, a favorite of the Dauphin, combining aspects of the trial by combat in its official sanction by the crown, as well as the duel of honor, being that the underpinning affront was simply a matter of defamation and the combat "asked for" by giving the lie.
At court one day, the Dauphin declared that Jarnac was a "kept man" by his step-mother, explicitly stating he was living off the woman's dime, and of course implying he was sleeping with her as well. His honor impugned, Jarnac had no recourse but to give the lie, but could not do so to the future King. La Châtaigneraye stepped in as champion, and stated that he had given the information to the Dauphin, having been told by Jarnac himself. Combat was requested of the King, Francois I, but refused, and instead only a court proceeding for defamation could continue. That is, until Francois I died a year later and the Dauphin assumed the throne as Henri II. La Châtaigneraye requested combat again, and it was granted.
Contrary to all expectations, however, La Châtaigneraye was defeated, despite being considered one of the best swordsmen in the country. Jarnac was the less skilled fighter, but in what would go down as the "coup de Jarnac", hamstrung his opponent with a slice to the back of the knee, ending the fight swiftly. Requesting the King grant his opponent mercy, Henri II, perhaps in shock, would not, remaining silent until Jarnac had asked three times for mercy to the defeated. Finally agreeing to give his erstwhile champion medical attention, it was too late. There were strong political underpinnings to the fight, and Henri II most certainly intended the victory of his champion to carry strong symbolism for the beginning of his reign. Supporters at court had split between family lines, with those against the king having supported Jarnac, as did almost every Protestant in France.
This would essentially be the end to the sanctioned duel. Henri II would never again grant the field, although he would not officially abolish the institution, and as we move into the 17th century, the honor duel became an illicit, entirely private combat.
Sources:
The Last Duel by Eric Jager is a very interesting book, covering the duel of Jean de Carogne and Jacques le Gris.
The Duel by Robert Baldick is a basic history, but offers a number of anecdotal examples of trials by combat in the medieval period.
The Duel: Its Rise and Fall in Early Modern France by Francois Billacois focuses mostly on the honor duel from the 16th century onwards, but includes a chapter on the duel between Jarnac and La Châtaigneraye.
The Duel in European History by VG Kiernan is a decent overview of the history of the duel, and touches on the antecedents, including trial by combat, early on.
These links may help until someone else qualified to answer comes along.