In this hypothetical universe, the speed of light is proportional to the local gravitational field strength. Here is the journey of the laser pulse as it approaches the black hole:

1. **Speed**: The speed of the laser pulse increases as it moves towards the black hole. This is because the gravitational field strength \( g \) increases near the black hole, and the speed of light \( c' \) is proportional to \( g \). Therefore, \( c' = k \cdot g \) (where \( k \) is a proportionality constant) results in a higher speed in regions of stronger gravity.

2. **Frequency**: The frequency of the laser pulse increases due to gravitational blueshift. As the pulse moves into a stronger gravitational field, it gains energy, which corresponds to an increase in frequency. This effect is similar to the gravitational blueshift observed in general relativity, where light gaining energy results in a higher frequency.

3. **Trajectory**: The trajectory of the laser pulse remains a straight line directed towards the black hole. Since the gravitational field is radial and the pulse is moving directly towards the black hole, there is no transverse component to the gravitational force that would cause deflection. The varying speed of light does not affect the direction of the pulse, maintaining a straight path.

### Final Answer
As the laser pulse approaches the black hole, its speed \boxed{increases} due to the stronger gravitational field, its frequency \boxed{increases} due to gravitational blueshift, and its trajectory remains a straight path towards the black hole.