mkdir h264vids
for f in *.mp4; do ffmpeg -i "$f" -map 0 -c copy -c:v libx264 -crf 23 -preset medium h264vids/"${f%.*}.mkv"; done

• Will output to a directory named h264vids.
• Assumes your inputs are .mp4. If not, change the .mp4 instance in the example to your input file type, or just use the greedy * by itself.
• Adjust -crf for quality and -preset for encoding speed/efficiency. Or just remove these options and use the defaults which are fairly good and should suffice for most (the example is using the default values for these options).

See FFmpeg Wiki: H.264 for more info on these options.