Does Firebird support full-text search?
Not directly in the engine, but there are 3rd party solutions:
http://www.ibobjects.com/ibofts.html
http://www.textolution.com/ftsib.asp
http://www.codeproject.com/cs/database/FulltextFirebird.asp
http://www.tamaracka.com/
http://sourceforge.net/projects/mutis
http://www.sphinxsearch.com/
There is a fork of Firebird code made by a company called Red Soft. It's licensed under the same license as Firebird, so you can take a look at their version which can support full-text searches using Lucene engine via JavaVM interfaces:
http://www.red-soft.biz/en/index.html
You can also read a paper titled "Full text search in Firebird without a full text search engine" by Bjoern Reimer and Dirk Baumeister, presented at 4th Firebird Conference:
http://www.ibphoenix.com/downloads/FirebirdConf2006/TECH-TPZ303-R/TECH-TPZ303-R.zip