Converting GIMP curves files to Photoshop (.acv) for ffmpeg
I ran into the same issue, so I threw together a Python script (posted and linked at the bottom). It doesn't convert the GIMP curves present into a .acv. But it does convert it directly into an argument for an ffmpeg curves video filter. I had hardcoded the files into the script, but to make it a bit more user friendly I added some instructinos and commandline inputs for the file-in and file-out. 

NB: If you are doing a simple -vf you can copy and paste it directly. If you are using a complex filter graph you still need to put the [in] and [out] arguements on either side. 

Here's a usage example: I've bolded the parts that you would need to add and ellipsed the very long filter statement. 

simple vf: ffmpeg -i videoin.mp4 -vf curves=master="0....1.000" videoout.mp4

part of complex filter that concatenates two videos, color corrects the product, and adds a separate audio track:

ffmpeg `
-i vid1.mp4 `
-ss 0:0:03.04 -i .\vid2.mp4 `
-i .\audio.m4a `
-filter_complex `
"[0:v][1:v] concat=n=2:v=1:a=0 [stitched]; `
[stitched] curves=master='0.0/0.000000 0.01171875/0.008608 `    
....0.99609375/1.000000' [stitchedcorrected]" `
-map '[stitchedcorrected]' -map 2:a:0 `
-vcodec libx264 -preset slow `
out.mp4


Hope this is helpful! Let me know if you need any help.

http://pythonfiddle.com/gimp-curves-to-ffmpeg-curves-arg/

import re

#make generator
lower=0
upper=1
length=256
zerotoonestepped256gen = [lower + x*(upper-lower)/length for x in range(length)]

def formatForFFMPEG(values):
    serializedValues = values.split(' ')
    list = []
    for i in range (len(serializedValues)):
        if not list or zerotoonestepped256gen[i] - float(re.match(r"^[^////]*",list[-1]).group(0)) &gt; 0.01:
            list.append('%s/%s' % (zerotoonestepped256gen[i], serializedValues[i]))
    return list

#print instructions
print('This is a tool to convert a color curves map from GIMP to a curves filter that can be inserted into the -complex_filter. Note that you still need to append the input and output streams onto either side of the command.')
#get filename
file = input('Please input the absolute path to the GIMP Color Curve Preset File: ')
out = input('Please enter the output file (file will be overwritten if it exists): ')

#Open the curves file
curvesfile = open(file,"r")
curvesString = curvesfile.read()
foundValues = re.findall(r'(?&lt;=samples 256) [\d. ]*',curvesString)

masterValues = formatForFFMPEG(foundValues[0][1:])
redValues = formatForFFMPEG(foundValues[1][1:])
greenValues = formatForFFMPEG(foundValues[2][1:])
blueValues = formatForFFMPEG(foundValues[3][1:])
alphaValues = formatForFFMPEG(foundValues[4][1:])

commandPrelim = 'curves=master="'

command = commandPrelim + ' '.join(masterValues) + '":red="' + ' '.join(redValues) +'":green="' + ' '.join(greenValues) + '":blue="' + ' '.join(blueValues) + '"'


with open(out, 'w') as out:
    out.write("Final Command\n\n" + command + '\n\n')
    out.write("master\n\n" + ' '.join(masterValues) + '\n\n')
    out.write("red\n\n" + ' '.join(redValues) + '\n\n')
    out.write("green\n\n" + ' '.join(greenValues) + '\n\n')
    out.write("blue\n\n" + ' '.join(blueValues) + '\n\n')
    out.write("alpha\n\n" + ' '.join(alphaValues) + '\n\n')