...The skinny road bike tires ...
Not much to those. Keep the tire pressure up. Use a pump with a pressure gauge until your thumb gets calibrated.
Invest more effort in "going light" for all foreseeable bumps. Should come naturally to an old MTBer - unless you're one of those who rode MTBs on roads for the looks of things.
..the old French gears are not something I'm really familiar with..
Not much to those either. But a pic or a make&model would make it easier to advise.
French can get a bit scary when things break.There are a couple of places on a bike where they preferred to use less common standards.
.. I'm not so confident in my bike...
In that case, handing it in to a reputable shop for a service and a tune-up would be a better fix than logging some trainer miles.
.. I'm not so confident in my .. cycling abilities anymore ...
Handling skills or stamina?
Making the pedals go round is about the only thing you train on a stationary bike, and that should be pretty far down on your list of concerns.
If you're simply feeling through-and-through rusty, find an empty parking lot somewhere.
Ride circles, figures-of-eights.
Go slow, practice tight turns. Both standing and seated.
Build some speed, practice braking.
The front should be your first choice.
Don't stop until a rear wheel lift no longer scares you.
Read up on the Rules of the Road.
And The Rules too:
http://www.velominati.com/the-rules/
Might want to check hand signs for pack/peloton riding too.
You never know when you pick up company.
..I'm not so confident in my .. cycling abilities anymore to be dealing with some of these hills.....
Many road bikes - even with freewheels, which I suspect yours is - are geared kinda high for the average guy.
But being out on the road is so much more rewarding than stationary riding that I suggest you go for it anyhow.
Enjoy your rookie status and use it to dismount w/o embarrassment when the going gets too tough.
Being stubborn here can easily lead to overexertion injuries, and a serious break in your training schedule.
.... Figured I'd build up a little strength before I get out there ..QUOTE]
Road riding in general isn't as much about strength as it is about stamina/endurance.
So keep your cadence - pedalling pace - in the 80-100 rpm range and your effort level where talking is getting difficult but doable and go at it.
Might want to start with fairly short sessions until your butt has gotten acclimatized to the saddle.
....before I get out there and show off....
If you deliberately try to show off, anything that happens is on you. That's an attitude that invites disaster.