Sorry it took me a while to reply to the thread, RL issues. Anywhere here's some thoughts and answers...
https://www.alternatehistory.com/forum/threads/ahc-a-valois-holy-roman-emperor.407521/
This thread includes my thoughts upon how this could happen. It is quite different than your POD
@Shiva , but yours works too.
Look up the TL in my signature, sometime the story will get to where he is Emperor.
(Not trying to advertise, just showing my future thoughts on Francis I's election)
Now for the actual effects (some of which I will include in my TL)
1. Severely blunted power of Habsburgs
2. MASSIVE FRANCE-WANK
3. Coalitions against France
4. Nearly constant war (see effects 2-3)
5. If Ferdinand is still around, he will fight for the throne. Alternately, he might be put in as replacement for sickly Charles.
I think your prompt offers more flexibility than mine, but other than a France that managed to absorb Netherlands-Burgundy and didn't antagonize the Electors with Italian Wars, I think Francis I was the French Kingdom's best shot at ever getting the HRE directly via an election.
After all there were no 'German' candidates available since RL's Ferdinand I was in Hungary at the time (and 16 to boot), Charles I of Spain, while technically a 'German-speaker' could also be called Burgundian/Dutch due to his lands in the HRE, and being King of Spain meant another foreign influence.
At least Francis I can claim to be a descendant of Charlemagne, but he is French and the Italian Wars of his ancestors are a stumbling block.
In RL it was Charles who snagged the prize, but as I noted if there was a major health scare that happened to him, like severe illness or injury then the distraction due to his condition could give Francis the opening needed to sway enough Electors to his side to win the Crown.
As for the effects here are some of my opinions.
Yes the power of the Habsburgs would be blunted, but in the immediate term they still hold Spain and all of the wealth pouring into the first 'Empire on which the Sun does not set', Ferdinand was due to inherit Hungary, and a wide range of lands in lands in the HRE that make up the Low Countries, Slovakia, and modern Austria, and pieces of modern Germany and Switzerland.
They can (and will) cause Francis I of the Holy Roman Empire and France endless grief.
Not to mention that the Ottoman Empire won't be forming an alliance with Francis, instead they might start cozying up to Spain to counteract Franco-German power, or try for a triple alliance with Poland and England against 'the Valois threat', offering Henry VIII help seizing back Aquitaine would be bait too sweet for Henry to resist.
Then with the unavoidable rise of Protestantism in both the HRE and France will be just as much an open sore and source of conflict as it was for the Habsburgs in this era.
But it's not all bad news, Francis will be in position to make good alliances between the German and Italian lords and himself, he can probably secure big chunks of Italy for the French crown through use of the HRE's legal system, some medievalism trickery, outright bribery with French gold, and good old fashion force. And yes I believe that Francis would rather secure Italy before anything else in the HRE since it's been an obsession of French foreign policy to get back 'their Italian lands' for some time in that era.
Not to mention that with the Protestants sinking deep roots in the Netherlands would make taking 'Burgundy' from the Habsburgs undesirable, except maybe to push Spain out of their vassal holdings in Francis's HRE...
Also along with being the Emperor he will be in a position to put more pressure on the Papacy, maybe even create a second Avignon Captivity.
As long as Francis can use the HRE's crabpot nature to the hilt, he can get a lot out of it, maybe even keep it for his heirs. But if he doesn't manage that, hey he can take comfort in squeezing the HRE for everything he can get before he dies.