[Captrek]

Melakon wrote:

---

Do we know whether Picard and Beverly had a relationship before she met Jack?

They did not. From Conspiracy:

KEEL: Do you recall the night you introduced Jack Crusher to Beverly?
PICARD: You know full well I hadn't even met Beverly then. You introduced them.

Here's some interesting story background from the novels:

From Memory Beta:

In 2354, the Stargazer encountered an unknown anomaly later termed a Nensi phenomenon, which crippled the ship and caused a dangerous energy build-up in the starboard warp nacelle. Crusher and Lieutenant Peter Joseph both volunteered to go outside the ship to detach the nacelle with phaser rifles. In the course of this operation, Crusher was caught in an explosion, though was successful in cutting the nacelle free. Joseph, who had panicked and left Crusher alone, feigned unconsciousness when he saw Picard on his way to retrieve his men, and allowed himself to be "rescued" while Crusher perished. Joseph later claimed both men had been overcome by the energy cycling in the nacelle. (TNG novel: Reunion)

If I remember it correctly, the situation Picard faced was similar to the one faced by Wesley in "Coming of Age" and by Spock in "Balance of Terror": he could have saved either man, but did not have enough time to save both. He rescued the one who was closer, which availed a higher probability of a successful rescue. That's the same triage decision made by Spock in BOT. Wesley made his choice on the basis of one of the two victims being uninjured and having an opportunity to save himself while the other one could only be saved by Wesley.