Both Uses of

coquette

in

A Tale of Two Cities

If I do—Well," said madame, drawing a breath and nodding her head with a stern kind of coquetry, "I'll use it!"†
Chpt 2.16

coquetry = casual playfulness that arouses sexual interest

The gaoler standing at his side, and the other gaolers moving about, who would have been well enough as to appearance in the ordinary exercise of their functions, looked so extravagantly coarse contrasted with sorrowing mothers and blooming daughters who were there—with the apparitions of the coquette, the young beauty, and the mature woman delicately bred—that the inversion of all experience and likelihood which the scene of shadows presented, was heightened to its utmost.†
Chpt 3.1 *

coquette = a woman who is casually playful in a way that arouses sexual interest of men

Definition:

a woman who is casually playful in a way that arouses sexual interest of men but does not imply serious flirtation

Coquette is a French word that is similar to the word flirt. There are two primary differences:

Coquette only refers to a woman whereas flirt can refer to either sex.
To say someone is coquettish implies that she is just being playful and does not intend sexual relations with the man with whom she is interacting; whereas when a woman is described as flirting, the word does not indicate whether she is just being playful or she wants to instigate sexual relations.