I have a pink champagne currant bush, but it's only in its second year, so I won't be getting enough fruit for winemaking just yet. But based on my elderberry wine experiment last year, here are some ideas:
1) You probably want around 4 lbs of fruit per gallon.
2) If you freeze the fruit first, it disrupts the cell structure and aids in extraction of the fruit goodness.
3) As others have said, check the acid levels. You probably want to shoot for a pH of 3.3-3.4.
4) For fruit (country) wines, it's generally recommended not to go for high alcohol if you don't want to overwhelm the fruit. An initial gravity of 1.08 to 1.09 would be good.
5) 71B is an all-around good choice for a fruit wine yeast.
6) After an initial 12-24 hours of K-meta, be sure to use an appropriate amount of pectic enzyme for the volume of wine you're making, and stir every few hours.
7) Add yeast nutrient and pitch the yeast 12-24 hours after adding the pectic enzyme.
If you have a spare carboy, give it a dose of K-meta and 3 months of bulk aging after secondary fermentation has finished. Top up with some dry Pinot Grigio or Chardonnay if needed. After 3 months, and before bottling, give it a taste. You can always back-sweeten, but you may discover that it's heading in a good direction as a dry fruit wine.