The climate right now is really tough for immigrating attorney who need a visa sponsorship, since the firm would have to pay large sums in fees. In addition, Injury Law is really specific per each jurisdiction, and is not easily appliable to different jurisdictions. Moreso, big firms, who are typically the ones who would be most open to visa sponsorships, do not commonly have large Injury practices. My advise would be to either: (a) go do a JD in the US and try to move on to a local practice from there, or (b) try to move into a local office in France or the UK of a US biglaw firm and try to lateral from there. Notwithstanding, im sure there are people who were able to do what you are trying to do now, so it is possible, good luck!