Plus you could remain an HRE member as far as I know.
You can. Did this as Muslim Poland. Actually works well because there's no risk of becoming emperor and losing the Imperial Integrity buff.

Although maintaining -100 piety is not really that practical. Besides losing it on every ruler change, most of the -piety decisions require the loss of prestige. Some give you gold as well (or instead) but it's typically not so useful. You also have the problem of gaining piety every time you attack a non-Sunni. Realistically if I'm going for negative piety I can probably hope to ride around -60 or -80, with occasional periods at -100.
More importantly, you really need to remain at 100% piety for a long time when you first convert, because you need to go back and convert all your original provinces which can take a while. Even with full Religious ideas it took me a few decades. Converting Kiev wasn't even possible until I happened to have the right combination of ruler (for Office of Sheik al-Islam decision) and 100% piety.
The upside is that the Hordes are extremely easy to diplo-vassalize.
Anyway, going Muslim as France would be pretty impractical compared to Bohemia, and you'd still have the -10% tech cost but worse NIs. France could obviously do it but you'd probably end up with a large amount of overseas territory. Tough to get a land connection to Africa or Asia as France, where Poland or Bohemia can do it a bit quicker.
As a side note you can retain a bunch of Catholic decisions (with varying degrees of usefulness...) like Statute in Restraint of Appeals, Witchcraft Act, Pass De Heretico Comburendo Act, etc when you convert to Islam because religion group switching doesn't remove them, just switching to Protestant does.