Eric Jaffe at The Atlantic Cities asked via Twitter last week: Should We Replace the Term ‘Congestion Pricing’? :

“Two favorites in my mind come from transport scholar David Levinson, who suggests road fees for general road pricing (and peak road fees for road pricing aimed at heavy congestion), and urban planner Laurence Lui, who recommends road fares. What’s nice about road fare is that it parallels mass transit, has an intuitive purpose, and offers flexibility. You can alter it to suit a specific situation — peak road fare, midtown road fare, etc. — without obscuring the basic meaning.”

The term “fare” definitely has a public transit connotation, its definition is: “The price of conveyance or passage in a bus, train, airplane, or other vehicle.”
The etymology is more general though:

fare (n.)
Old English fær “journey, road, passage, expedition,” strong neuter of faran “to journey” (see fare (v.)); merged with faru “journey, expedition, companions, baggage,” strong fem. of faran. Original sense is obsolete, except in compounds (wayfarer, sea-faring, etc.) Meaning “food provided” is c.1200; that of “conveyance” appears in Scottish early 15c. and led to sense of “payment for passage” (1510s).

On the other-hand fee comes from

fee (n.)
late 13c., from Old French fieu, fief “fief, possession, holding, domain; feudal duties, payment,” from Medieval Latin feodum “land or other property whose use is granted in return for service,” widely said to be from Frankish *fehu-od “payment-estate,” or a similar Germanic compound, in which the first element is cognate with Old English feoh “money, movable property, cattle” (also German Vieh “cattle,” Gothic faihu “money, fortune”), from PIE *peku- “cattle” (cf. Sanskrit pasu, Lithuanian pekus “cattle;” Latin pecu “cattle,” pecunia “money, property”); second element similar to Old English ead “wealth.”
OED rejects this, and suggests a simple adaptation of Germanic fehu, leaving the Medieval Latin -d- unexplained. Sense of “payment for services” first recorded late 14c. Fee-simple is “absolute ownership,” as opposed to fee-tail “entailed ownership,” inheritance limited to some particular class of heirs (second element from Old French taillir “to cut, to limit”).

I could go either way, but I think “fee” is better established and more likely to be adopted.