Going to Paris for a week in late December. I have free wi-fi in the apartment Im renting. If Im planning to turn airplane mode on to take advantage of accessing emails etc: can I also download SKYPE to make inexpensive calls to the US? Thanks

You need to turn of mobile internet and roaming. Airplane mode disconnect WiFi too.
There is a Skype app you can download.

If whomever you're planning on calling in the US has an iPhone or iPad, you can message them for free when in a WiFi zone, but Skype works fine. If you're with AT&T, they have their own VoIP app called AT&T Call International that you can download.

One thing you need to do is to tell your service provider you'll be traveling outside of the States. They will need to authorize its use outside of the country, otherwise you could end up without any service.

When we have rented apartments in Paris, telephone calls from the landline in the apartment include free calls to the US. Just ask the apartment owner or agent about this feature.

If you leave airplane mode ON then you are turning OFF everything - voice, text message, and data.

To make sure you don't inadvertently use data roaming or cellular data when you turn on your iphone, and to only use WIFI or else do not connect at all, do the following before you step on the airplane:

1) Turn Data Roaming OFF - so that your cellphone cannot connect to a 3rd party cellular carrier.
In iPhone5 this is via Settings --> General --> Cellular ---> Data Roaming -->OFF

2) Turn Cellular Data OFF - this will turn off cellular data, forcing it to use WIFI or else don't connect at all.
Voice and text message will still be on.
(For text message if you did not initiate the message, you won't be charged the international fee at all.)
In iPhone5 this is via Settings --> General --> Cellular ---> Cellular Data -->OFF.

On the new iOS7, turning things off is found through:

Settings > Cellular > Cellular Data and/or Data Roaming off.

No "General" step. This is near the top of the page.

I've read suggestions to Reset Statistics, which is at the bottom of the page, so you can see what you've done while on vacation.