For 2d lighting, you can just draw a lightmap every frame.
1. Create an image equal to the size of the backbuffer (create only once during initialization)
2. Clear the screen with black
3. Use additive blending to draw on light sprites (stretch to increase size, increase color closer to 255/255/255 to increase intensity)
4. Draw all the lights
5. Copy the backbuffer to your lightmap image
6. Clear the screen, draw as normal
7. After you finish drawing, draw your lightmap on top of the screen using Multiply blending
Very simple but versatile 2d lighting using just SFML.