If the wiznet chip is connected to SPI you can add a few lines to set the CS lines of the ethernet and sdcard alternating high.
something like
digitalWrite(CC_ET, LOW);
digitalWrite(CC_SD, HIGH);
string = file.readstring();
digitalWrite(CC_SD, LOW);
digitalWrite(CC_ET, HIGH);
client.println(string);
allways do the low first before setting the next to high...