Wasn't his objective to rule Scotland so he could have a free hand in France?
He started messing with them long before there were any issues in France.
Prior to this, Richard I had decreed that the English would totally recognise Scotlands independence, compared to before when they had suggested that the Scottish king was actually subservient to the English one.
Edward I grew up believing that the facts were that the Scottish were subservient, and Richard was simply being nice to them, whilst the Scottish believed that they had always been independent, and that Richard I had recognised this fact.
Also, there was little issue of the Scots causing trouble, at least before the chances of civil war between Baliol and Bruce, the border had been decided on in Henry's time.
But even so, the Scots regularly had to politely refuse invitations by English kings, or publicly (but again politely) remind the King of their independence. Alexander did so on his wedding day, and did so again when Alexander was obliged to do homage to Edward as a landowner in England.
Therefore, when it was suggested after Alexander died that Edwards son marry the Maid of Norway, he saw an opportunity not only to secure his own borders from the violence of a Scottish civil war, but to pave the way for an Englishman to rule a united Kingdom, stretching from the channel to the North Sea.
After Margaret died however, there was still the issue of civil war in Scotland. Robert the Bruce stated in a letter that if Edward assisted him in taking the throne, Robert would be willing to accept that Scotland was subservient to England.
My POD would be that Edward did not believe him, accurately judging from past experience and from the experience of his father that the Scottish would never accept English rule, and that any Scottish king who did try to state his subservience to England would have to fight against his own lords, opening up Edwards lands to the danger of a Scottish civil war. Thus, he concluded that trying was pointless, but, if he put Baliol on the throne, Bruce would probably try and rebel against him. If that happened, Edward could offer his "assistance" against Bruce, and then use that opportunity to get more concessions from the Scots. Land, money etc.