if you use the Intel IoT development kit SD card image for Galileo you will find libmraa which abstracts GPIO, i2c, ... and supports C/C++, Python and Node.JS out of the box
To answer your question about if the Wire Library of Arduino can be used on a C application, well, the libraries included in Intel's Arduino IDE are .h and .cpp so I believe they could be used on a C application, however I believe they would have to be modified and would probably require work (maybe a lot) to make it work. That being said, there are a couple of alternatives, for example you could use MRAA to interact with I2; MRAA is a C/C++ library made to interact with the Galileo/Edison's I/O interface. You can learn more about MRAA here:
Also you can check intel-iot-devkit/mraa · GitHub for some examples of using MRAA.
Another way of using I2C would be using I2C-tools, which is a package you can get from AlexT's repo.