I'm thinking about making two separate one-week trips into the Schengen area, the first to Germany and the second to France. The whole duration of both trips together lie within 90 days. I'm afraid that if I wait until after the first trip to apply for the visa for the second trip, it won't be in time. Can I apply to the German embassy for a double-entry visa, or what should I do?
If you have enough documents to prove the content of your second journey already when applying for the first trip's visa, then you can almost certainly get the visa to cover the whole period with no additional overhead. This means, you should know the dates you'll be traveling to France, preferably have flight tickets already booked, maybe even a few hotel reservations if you want to increase your chance. A one-year multiple-entry visa to Schengen area with a maximum of 90 days you can spend there in each 180-day period is not uncommon, I've seen up to 3-year visas with these conditions, so yours should not be a problem. The key to getting the visa you need is, as I mentioned already, being able to provide all the information necessary with correct documents when applying for the visa.
double-entry visabut multiple entry visa. You should apply for the multiple entry visa. But whether they give you or not, it is their prerogative. But if your finances are in order and you have a good previous Schengen record, it would help your case a lot.