Shipyards require a ridiculously high Naval Tech level, 16 I think. If you haven't seen any explorers or conquistadors yet, you're nowhere near that level. But check your message setting and your capital/major ports to be sure a nifty leader didn't sneak into the game without your knowledge (happened to me).
But for shipyards, the Spanish have a nice one in convenient Andalucia...if it happens to be lightly defended...and you happen to be at war... It's also within nice striking distance of Madrid, which would help make future Spanish wars almost trivial (moreso if you can take Toledo, too). Who cares about the permanent casus belli such possession would give them, if you hold a gun at their head. In the regular CG, Ragusa also has one, but that is a little out of your way and would involve an expensive (to Badboy) annexation; but the ICG removed that one anyway, if you're playing that version.
I'm not necessarily recommending Protestantism for France, but if you're thinking about changing to Protestant...now is the time to do it. Your stability can't get any worse and that's really the biggest hit to conversion. Also, if you're already that low on stability, you might as consider doing all the other nasty things that hit stability: raise the 6-month war taxes at a minimum, the additional penalty is non-existent; if there is anyone you've been meaning to attack, might as well do it now (but you need -2, rather than -3 to do this); even attacks against people you've got the 5 year peace (this will also effect your reputation, but the religion change is going to send some relationships toward -200 anyway). And, actually, being at war while converting is somewhat helpful...you don't seem to lose the alliances and vassals (not sure if it is a bug or a feature), which also seems to translate into a smaller relations penalty, and the loss of fewer diplomats. But remember, Protestants recover stability a bit slower than other nations (do you have a Fine Arts Academy, that helps a lot).
I don't buy into the theory that if you're targetting Calvinism, you should wait and do both changes at once. Since France is predominantly Catholic, I would assume the motivation for changing religions would be the extra settlers. So why lose 30+ settlers waiting around for a religious event? 30 years is plenty of time to resurrect your stability IMHO (although it'll be a bit slower since most of your provinces will still be Catholic - I think the latest patch gives an extra penalty). After conversion, you should max out stability, anyway.
The easy answer to settlers, though, is be patient. France should be getting a few, once its colonial dynamism starts to kick in. The number changes, and I believe it gets fewer than the other major colonial powers, but if you combine it with Calvinism and Andalucia...you should have no problems.
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