How to open old GOES-1 satellite image files downloaded from NOAA CLASS
Unfortunately, the older weather satellite data is, the harder it is to read. 
Perhaps NOAA's Weather and Climate Toolkit can open it.

The old stuff usually comes in tightly packed binary formats that may or may not be well documented (these satellites were designed to take pictures of clouds for weather forecasters to use, us future generations were more or less an afterthought).  Just to illustrate the difficulty: I've previously worked with data from the NOAA HIRS instrument from the late 1970s/early 1980s, and found that the headers contained a mixture of ASCII and EBCDIC information, and that some necessary calibration parameters for the thermistors on the on-board internal warm calibration target were simply lost, and that for some satellites, the available header documentation did not match what was actually in there, and I couldn't read most of the headers.  Other information useful for interpretation existed in the NOAA library, but was unavailable to me due to export restrictions (ITAR).

The imager on the first generation GOES satellites is the Visible-Infrared Spin Scan Radiometer (VISSR, flown on GOES-1–3 between 1975 and 1993.  A similar instrument with the same name has flown on several Japanese HIMAWARI GMS satellites between 1977 and 2000.

Pytroll is a series of Python packages to read and process satellite data.  It includes Satpy, which can read a large number of meteorological satellite imager data formats.  I think that anything that can be read by Satpy should be openable by the Satellite Information Familiarization Toolkit (SIFT), under development at the University of Wisconsin-Madison.  

Unfortunately, I don't think Satpy has a reader for GOES VISSR (most focus is on current and future instruments), although there are plans for GMS VISSR (I don't know why this issue was closed).  Considering the similarity of the instruments, a reader for one should hopefully be similar to a reader for the other.  At least for GMS VISSR, file format documentation is available.  For GOES VISSR, some information appears retained at CEDA, but unfortunately that appears to be lacking in the detail you would need.

If you plan to develop a reading routine (you'd need to learn Python first if you don't know it already), do hop in to the Pytroll slack for advice.  There are also Pytroll workshops (normally twice a year) that are a great resource if you intend to work on a new satellite reader.

There might exist propriety software that can read this data, but unless you work at an employer that holds a license for such, that is going to be difficult to access.