Why would you rotate the
axis?
Just align the missile's velocity vector with the ship's direction vector. Maybe the
Thor.Vectors module can help you, it contains many utility functions, e.g. to rotate, project or multiply vectors.
With Thor, you can get the direction from a rotation angle as follows (2 possibilities):
sf::Vector2f direction = thor::PolarVector2f(length, angle);
sf::Vector2f direction = thor::rotatedVector(sf::Vector2f(length, 0), angle);
Given a direction vector from a ship, the missile's velocity is then just a scaled version of it:
const float missileSpeed = ...;
sf::Vector2f shipDirection = ...;
sf::Vector2f missileVelocity = missileSpeed * thor::unitVector(shipDirection);
Of course, you can also do this in one step if you store rather a rotation angle than a direction vector in the ship.