Were 16 in Wheels an option on a 1978 308?

Yes, they were available as an option, with Pirelli tyres, starting end 1977. Could be fitted to an earlier car, of course.
Rgds

http://www.308-328.com/308/308spectechcarben.html

 

What is the size of your spare tire? If it’s 14” then more likely your 16” are not original, or better yet, what does the tire info label On the car says?

 

What year did they move to full-size spares? The early cars add the space saver size.

 

The SPCs for 1978 B/S indicate that it was "version" thing:
euro (standard) version = 14" or 16" (and car with 14" had the space saver spare while a car with 16" had a 7x16 full size spare)
US version = 14" only (and 5th 14" full size spare)
but a US Dealer could probably get 16" to close a sale.

In your photo, if those are photos of the actual wheels on the car , it looks like those are OE stock 16" wheels so way more valuable than stock 14" -- and this should have zero impact on your decision as a set of 14" isn't big money to get if you want them and the OE 16" can be sold for big money -- JMO.

 

As Steve and others say, those 16"s are legit, they have date codes on them maybe.

As to the spare, my #22127 came with a Dino wheel spare, 14" as it was bought. I was upset it "Didn't match" but it was likely OEM.
Also as noted a 14" rim in 6.5" or 7.5" will fit an early car.

I doubt the rear 16" would go in and as Steve posts a 16" x 7" would be the spare in that case.