A: Great question, Ronald. In most cases old 10-speeds like yours can be tuned-up fairly inexpensively and will ride just as nicely as they did when they were new. I actually had a few Peugeots and would guess that you probably have a Peugeot AO-8 or UO-8, which were very popular bikes in the 1970s. I found a photo and catalog page of the first UO-8 so you can get an idea how it looked when new. It's from 1963, but the bikes didn't change too much.
The easiest thing might be to bring your bicycle into your local bicycle shop and have them tune it up. They should have the 27-inch tires if you need new ones (actually, these are pretty widely sold, even at some hardware and department stores), and they'll have brakes shoes, cables, new handlebar tape and the skills to lubricate the drivetrain, brake and derailleur pivots, true the wheels and fine-tune the shifting and braking.
Or, if you want to do the job yourself, you might find that if you simply pump up the tires, lightly lubricate the brake and derailleur pivots and the chain, the bike will be rideable. As long as it hasn't been stored in direct sunlight or in a damp place, it's possible that the tires, though tired looking, might have some life left in them. And, the tubes, which are protected by the tires should be fine, too. If the bike's been sitting that long the air will have leaked out but if you pump up the tires you might get lucky and find they hold air. Then you can test ride the bike gently and see what other repairs it needs. If it's anything you can't handle you can visit the shop and have a pro help you.
Keep in mind that you'll want a safe bike for riding to work around cars so be sure the brakes are working well. Often on an older bike the rubber brake pads harden. They may look fine but over the years they get too hard to grip the rims and offer much stopping power. It's usually a good idea to replace them. You'll also want reliable shifting so you can get up the hills and don't drop the chain. Shifting it on an easy ride around the neighborhood should tell you whether adjustments are needed, or not. If you're not sure, head to your local shop or follow these derailleur instructions on my site.
A few other tips: unless you can bring you bicycle into work with you, be sure to get a good lock, carry it with you and use it to protect your bike. Just because it's old doesn't mean it won't get stolen. Locks come with brackets that make it easy to carry it on your bike. Another helpful accessory for cycling commuters is a rear rack that you can attach a bag to to carry your lunch, a change of clothes, a laptop, etc. Or, you might choose to carry these essentials in a backpack or messenger's bag. The rack and bag make more sense if you're riding long distances. Carrying your gear works fine for shorter rides. But, as you ride further you can get sweaty and even a sore back if you're carrying enough stuff. When it's on the bike you hardly notice it. Lastly, ride safe. For example, a lot of people don't realize that when you ride on the road you should always ride with traffic never against and always obey the traffic laws so that you don't get hit. Most of the time you can find parallel routes to the busy ones that are more peaceful and fun to ride on, too. Here again your local bike shop should be able to recommend great routes for avoiding traffic choked roads.
Hope these tips help and you save a lot on gas costs. I bet you enjoy biking to work so much you do it more than you think,