Both the .docx and .fodt files are documents so docx to fodt conversion should be doable. Your best bet would be some OpenOffice.org based word processors as these should support both of these file types just fine. Maybe some online based document converters might be of help as well.
Home > Search converters: docx to fodt
Conversion of docx file format to fodt file format beta
Search for docx to fodt converter or software able to handle these file types.
Convert Microsoft Word Open XML document to OpenDocument Flat XML document.
We have found 3 software records in our database eligible for .docx to .fodt file format conversion.
Apple macOS / Mac OS X software 
- convert docx to fodt on OS X
NeoOffice
A full-featured set of office applications for Mac
File extension | Convert | Open | Save | Edit | Create | Import | Export | Extract |
|---|---|---|---|---|---|---|---|---|
Convert from docx file | No | Yes | No | docx editor | No | No | No | No |
to fodt file | No | Yes | Yes | fodt editor | No | No | No | No |
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned docx to fodt. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Multiplatform software 
- convert docx to fodt on any platform
Apache OpenOffice Writer (OpenOffice.org Writer)
Word processor and text editor from OpenOffice.org suite
LibreOffice Writer
Full-featured word processing and desktop publishing tool from LibreOffice suite
Additional links: Open docx file, Open fodt file
DOCX
Files with docx extension are documents written and saved using Microsoft Word word processor edition 2007 or later. DOCX format replaced the previously used DOC format, moving from binary files to Open XML schema-based documents. They are supported in almost every modern word-processing tools.
FODT
Files with fodt file extension can be typically encountered as documents saved in OpenDocument Flat XML document in any of the OpenDocument schema based productivity suites, such as OpenOffice.org or LibreOffice.
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