I prefer 'milieux' in the plural and a good term would be 'issues de', if not 'origniaires des'. I would prefer a sentence such as: Ces femmes issues de milieux populaires + verb, but that may require you to play too much with sentence structure and emphasise. Anyway, grassroots is the bottom of a hiearchical pyramid, the first rung of the ladder and the most crowded one. 'Populaire' is a good term, although in a political setting (grassroot support for a party leader) you might use the term 'militant', i.e. someone actively involved in the life of the party locally, but not necessarily one of the silent or silenced majority implied by the 'working masses' socio-economic connotations of this term. Sorry for rambling ;-)