Do airlines for which you work for provide free training for their aircraft type ratings and EASA conversion?
US based airlines will provide the aircraft type training. What exactly do you mean by EASA conversion? Do you have foreign licenses now that you would like to convert to FAA licenses?
As Chris said the airlines will train in type you in the airplane(s) you’ll be flying. They will not however provide a EASA conversion, that’s on you which is why ALL US carriers require FAA licenses for employment.
I think question should be what is an EASA conversion useful for?
An EASA conversion is required if you want to fly for certain European Union carriers. Since you initially asked the question I think we assumed you knew.
Do American airlines that fly to Europe require this EASA conversion?
No. US based airlines operate under FAA certification standards. Such is the same for other countries, for example an Air France pilot utilizes his European license when flying to the US. He is not required to get an FAA license to fly here.
As Chris said, the EASA is only required to be EMPLOYED by that airline IN that country, but not to fly to/from those countries and that makes sense. Kind of like if you go on vacation in Europe you can drive there for a period of time but if you actually move to that country you will have to get their driver’s license. Otherwise International pilots would have to carry a wallet full of licenses. Make sense?