Moving to Brussels - two girls 10 and 7 - very little French/no Dutch - advice please

From personal experience and other comments here, it takes about 6 months for them to get fairly fluent in the language if thrown into it. Your choice of state school will be limited to the area that you will live in. There will normally be some support but it will vary in quality.
Extra lessons before you come would be advisable. Maybe see if you can find a French au pair to come and live with you. They want to learn English so it can become a fun exchange.
When you arrive, schools finish around 3.30pm (12.30 on Wednesdays) Find somebody local to pick them up and help with language and with homework for a couple of hours.
Private schools are out of most peoples’ price range unless the company is paying. There is a hybrid state/private school near Wavre, south east of Brussels, called Le Verseau which costs about 10% of the private schools and is very used to handling your situation.

I had rather thought that you would receive more replies than Wezembeekwanderer's helpful contribution so I have refrained from responding up till now. However it isn't clear whether you are aware of the background to education provision within and near Bruxelles and since that could have some important implications on where you choose to live, I will try to outline the situation.

The nominally bilingual Bruxelles-Capitale-Région comprises 17 communes which lie almost totally within the Brussel Ring R0 (and for the most part don't actually reach out quite as far as the Ring). These communes are, by and large, very polyglot but officially have around 85% francophone and 15% nederlandophone residents based on the language of their identity cards although the percentages vary by commune and no official figures are issued. Teaching at any one school will be in one language or the other although both languages are taught to every pupil from about age 8 upwards. The schooling is split between Maternelle (starts at 2½), Primaire (6 upwards) and Secondaire (12 upwards) and is compulsory from age 5 upwards. Francophone schooling is overseen by the Federation Wallonie Bruxelles and nderlandophone schooling by the Flemish government but the actual schools are provided by a number of bodies, for example Communes and the Catholic Church. The FWB is currently making a number of changes to the schooling it provides and this includes the school year which will comprise five terms with a seven (instead of nine) week summer break and four other breaks of two weeks. Schooling is compulsory so family breaks and holidays have to be taken during the school holidays. Francophone schools in Bruxelles are very used to taking pupils who speak little French and who consequently need extra support. Such pupils, particularly the older ones, may have to be put back a year but this is a normal feature of the Belgian education system anyway and shouldn't have any longterm downsides. Generally the Belgian public education system is excellent although `Bruxelles suffers to some extent from mushrooming demand.

Outside the 17 Bruxelles communes all the communes a re officially Dutch-speaking although six have a sufficiently high percentage of French speakers to be required to provide some francophone schools, these are
Drogenbos, Kraainem (Crainhem), Linkebeek, Sint-Genesius-Rode (Rhode-Saint-Genèse), Wemmel and Wezembeek-Oppem. Beyond the Flemish communes to the immediate south of Bruxelles lie the numerous communes of francophone Wallonie; schools there offer the facility to learn Dutch but it isn't compulsory, English being a common alternative. Language learning in Belgian secondary schools is exemplary, especially when compared with the UK, and that could well be said of the rest of the curriculum too, with technical as well as academic subjects well covered.