I just got this script to do what you want:
def panToExtent(gmapsLonLat):
mxd = arcpy.mapping.MapDocument('CURRENT')
dataFrame = arcpy.mapping.ListDataFrames(mxd)[0]
lat, lon = gmapsLonLat.split(',')
lat = float(lat)
lon = float(lon)
extent = arcpy.Extent(lon, lat, lon, lat)
dataFrame.panToExtent(extent)
arcpy.RefreshActiveView()
Save it somewhere and then load it in the Python console window (right-click > Load).
Then you can simply call the function:
panToExtent('49.616170, 6.140333')
You have asked to enter it as a string, so I wrote it that way, but that also means that you have to paste your coordinates into a string, so do not forget to add the quotes!
To make it even more comfortable, I would not bother adding it as a string, and perhaps use the following code:
def panToExtent(lat,lon):
mxd = arcpy.mapping.MapDocument('CURRENT')
dataFrame = arcpy.mapping.ListDataFrames(mxd)[0]
extent = arcpy.Extent(lon, lat, lon, lat)
dataFrame.panToExtent(extent)
arcpy.RefreshActiveView()
Now you can simply copy from Google Maps, and paste everything into your function when you call it, such as here:
panToExtent(50.850342, 4.363153)