Respectively, I would think so, probably much the same, he was such a treacherous idiot, and depends on the outcome of the negotiations and on Edward's will in the matter I suppose. The princess involved was not as such a French princess, but was
Bona of Savoy. She was the preferred choice of Louis XI, who wanted to take Edward away from a Burgundian alliance. Louis had flattered and bribed Warwick into supporting his choice, but Edward himself favoured Burgundy. Could have gone either way, but if it had gone as Warwick wished his loyalty would have been assured for a while, nor would that of others have been strained as it was by a romantic but very foolish and irresponsible marriage, all done behind the backs of Edward's family and counsellors.
Other possible consequences. without Warwick's support the case of Henry VI and his family would have been even more dire than it was. On the other hand, the different course of events might have led to Henry's son, and even Henry himself, still being alive when Edward IV died leaving a minor heir, and scope for either a Lancastrian restoration or Gloucester's usurpation as in OTL. Probably. Obviously Edward V would never have existed, and one would naturally assume that any heir from the Savoy or other marriage would have been even younger than he was on accession. But in fact although such a marriage would have taken place later than the one to Elizabeth Woodville, the older children were all girls and Edward V was not born until six years after the marriage. Edward IV could well have married someone else say a year later, and had a son four years earlier, 16 rather than 12 on accession, making a huge difference. If it were Bona and he married her in 1465, she would have been 16 and the marriage could have been consummated straight away, with a son born in 1466 rather than 1470 as Edward V was.
So as usual the consequences would all depend, but could end up saving a lot of bloodshed in various Roses battles, while eliminating the Tudor succession and the historical and Shakespeare's Richard III alike. The reign of the historical one, that is, not his existence as Duke of Gloucester.