In RJ Knecht's "Renaissance Warrior and Patron," about Francis I, he makes mention of archers in Francis' army, who he says fought with lances. That seems bizarre to me that soldiers deemed "archers" would have lances as their primary weapons. Is there a reason that they were called archers? Or is Knecht faulty on this?
Knecht is right, but I understand your confusion. Would it have killed him to add one or two sentences of explanation to that section?
Your source is referring to the archers in the lances fournies in the compagnies d'ordonnance that became the mainstay of the French army at the end of the middle ages. This "lance" is not a weapon, but a unit organisation: a squad, if you will, consisting of a mounted man-at-arms, ("knight" in the popular imagination, a heavily armoured horseman) two or three mounted archers and a number of lighter auxiliaries. Such 'lances,' or their equivalent, feature in all kinds of places in European warfare in this period, though their actual composition changes from time to time, and from place to place.
Now, the confusing bits: Originally, these units had worked like you'd imagine; one horseman with a lance supported by some more lightly equipped horsemen with bows or crossbows. However, over time these "mounted archers" started evolving into lancers themselves, but the original name stuck. In later eras, "archer" simply meant a slightly lower class of armoured lancer than the man-at-arms.
Even the "lance" itself wasn't really used as a battlefield organisation any longer by the time of Francis I, and units operated in companies instead. The term persisted as an administrative feature, though.
So the answer is that you're dealing with legacy terms.
Though, to add even more confusion, the Italian Wars themselves consist of something of a transition period in this development, and sources from 1490 still state that archers should be able to shoot, and there are still decrees demanding bows be made for the archers in 1515 and 1526, though it's very likely that the "archers" were already mostly slightly-less-heavy-cavalry by this stage. In the ordinance of 1549, the archers are to have almost the same amount of armour as the man-at-arms, with the addition of a 'pistolet.' There are no more mentions of actual bows or crossbows after that.
Source: Potter, David. Renaissance France at War : Armies, Culture and Society, C.1480-1560. Woodbridge: Boydell Press, 2008, (pp. 78-80).