I'm guessing you like the sweeter style of sparkling wines, and the difference between that, white zinfandel (almost always sweet), and red wines can be huge.
Cabernet can be pretty intense I'll agree, and a big departure from your favorites. If you want to try some reds, here are some ideas in the smoother category.
Look for Zinfandel (it'll be dark, not pink), from easy to find makers Ridge or Seghesio. Expect these to run from $15-$25. Also, Australian Shiraz can be quite easy to drink. There are many nice options for under $20. Yellow Tail Reserve (make sure it's the reserve) is tasty enough. Or upgrade to something like Yangarra or Kilikanoon Shiraz for a bit more cash. California Syrah (different word for Shiraz) is worth a look. The 6th Sense Syrah (reddish label) is a good blend, and commonly found for about $16.
Merlot is another nice grape to look at. It's sort of a kinder, gentler cousin of the Cabernet Sauvignon grape. Columbia Crest's Grand Estates is a killer merlot for $10-$12, get the 2004 version if you can find it, but any you see will be fine.
But, I suspect that even these reds might be tough to get used to, at least initially. In that case, try some other light colored wines, like Sauvignon Blanc (most New Zealand $15 SB will be pretty good), or California Riesling (I'd bet you'd like Pacific Rim Riesling by Bonny Doon). Then, work into Chardonnays, which are richer and often drier (less sweet). The more robust and drier white wines might be your best way to work into reds.
And, lastly, don't forget to try new wines with some food. It can help things along. Don't worry about perfect food/wine pairings, just get some good pizza or a block of parmesan cheese and olive oil/bread when you try the reds and maybe your seafood of choice or some salad with a tangy dressing when you have the white wines.
Only your palate knows for sure.